.MCAD 304020000 1 74 1937 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
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0 1 1 0 1 1 NO-TRACE-STRING
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0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
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.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
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.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
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.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
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.TXT 4 1 1472 0 0
Cg a73.000000,73.000000,21
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 File 
Name: filter.mcd}}
.TXT 4 0 384 0 0
Cg a72.000000,72.000000,106
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Copyright 1995.\par This program is written by Professor James S. Kang 
of ECE Department at Cal Poly, Pomona.\par }}
.TXT 8 0 397 0 0
Cg a73.000000,73.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Designing analog and iir digital filters.}}
.TXT 5 0 601 0 0
Cg a73.000000,73.000000,23
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
ENTERING SPECIFICATIONS}}
.EQN 5 0 527 0 0
{0:type}NAME:3
.TXT 0 9 528 0 0
Cg a64.000000,64.000000,99
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 type 
1: lowpass filter, type 2: highpass filter, type 3: bandpass filter, 
\par type 4: bandstop filter.}}
.EQN 6 -9 529 0 0
{0:ap}NAME:1
.TXT 0 11 531 0 0
Cg a62.000000,62.000000,76
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 ap 1: 
Butterworth, ap 2: Chebyshev, ap 3: Inverse Chebyshev,\par ap 4: Elliptic.}}
.EQN 6 -11 532 0 0
{0:case}NAME:1
.TXT 0 9 533 0 0
Cg a61.000000,61.000000,166
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 case 
1: specifications are given in terms of attenuations amax, amin and 
various frequencies.\par case 2: specifications are given in terms of 
order and cutoff frequency.}}
.EQN 8 -9 1169 0 0
{0:analog}NAME:2
.TXT 0 11 1170 0 0
Cg a62.000000,62.000000,86
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Set 
analog = 1 for analog filter design, and set analog = 2 for digital 
filter design.}}
.EQN 4 -11 1177 0 0
{0:iit}NAME:2
.TXT 0 10 1178 0 0
Cg a63.000000,63.000000,95
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Set 
iit = 1 for impulse invariant transformation, and set iit = 2 for 
bilinear \par transformation.}}
.EQN 6 -10 535 0 0
{0:amax}NAME:3
.TXT 0 14 536 0 0
Cg a59.000000,59.000000,58
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 amax 
is the maximum loss in dB in the pass band for case 1}}
.EQN 4 -14 537 0 0
{0:amin}NAME:6
.TXT 0 14 538 0 0
Cg a59.000000,59.000000,58
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 amin 
is the minimum loss in dB in the stop band for case 1}}
.EQN 4 -14 516 0 0
{0:N2}NAME:2
.TXT 0 14 517 0 0
Cg a61.000000,61.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 N2 is 
the order of the filter for case 2.}}
.EQN 4 -14 1171 0 0
{0:fs}NAME:10
.TXT 0 14 1172 0 0
Cg a59.000000,59.000000,67
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fs is 
the sampling rate in Hz. fs is used in digital filter design.}}
.EQN 4 -14 1173 0 0
{0:Ts}NAME:(1)/({0:fs}NAME)
.TXT 0 14 1473 0 0
Cg a59.000000,59.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Ts is 
the sampling interval.}}
.TXT 5 -14 534 0 0
Cg a73.000000,73.000000,34
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Specifications for lowpass filter.}}
.EQN 3 0 518 0 0
{0:fclpf}NAME:1000
.TXT 0 14 519 0 0
Cg a61.000000,61.000000,47
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fclpf 
is the cutoff frequency in Hz for case 2.}}
.EQN 5 -14 151 0 0
{0:fplpf}NAME:2.5
.TXT 0 14 152 0 0
Cg a59.000000,59.000000,55
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fplpf 
is the passband cutoff frequency in Hz for case 1}}
.EQN 5 -14 153 0 0
{0:fslpf}NAME:3.5
.TXT 0 14 154 0 0
Cg a59.000000,59.000000,65
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fslpf 
is the stopband cutoff frequency in Hz (fs > fp) for case 1}}
.EQN 4 -14 1821 0 0
{0:\qclpf}NAME:2*{0:\p}NAME*{0:fclpf}NAME*{0:Ts}NAME
.EQN 0 17 1822 0 0
{0:\qplpf}NAME:2*{0:\p}NAME*{0:fplpf}NAME*{0:Ts}NAME
.EQN 0 18 1823 0 0
{0:\qslpf}NAME:2*{0:\p}NAME*{0:fslpf}NAME*{0:Ts}NAME
.EQN 0 17 1907 0 0
{0:\qplpf}NAME={0}?_n_u_l_l_
.EQN 4 0 1908 0 0
{0:\qslpf}NAME={0}?_n_u_l_l_
.EQN 1 -52 1820 0 0
{0:\wclpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qclpf}NAME)/(2)),2*{0:\p}NAME*{0:fclpf}NAME)
.EQN 12 0 1180 0 0
{0:\wplpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qplpf}NAME)/(2)),2*{0:\p}NAME*{0:fplpf}NAME)
.EQN 1 52 1910 0 0
{0:\wplpf}NAME={0}?_n_u_l_l_
.EQN 5 -52 1181 0 0
{0:\wslpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qslpf}NAME)/(2)),2*{0:\p}NAME*{0:fslpf}NAME)
.EQN 2 52 1911 0 0
{0:\wslpf}NAME={0}?_n_u_l_l_
.TXT 4 -52 539 0 0
Cg a73.000000,73.000000,35
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Specifications for highpass filter.}}
.EQN 5 0 540 0 0
{0:fchpf}NAME:1000
.TXT 0 14 541 0 0
Cg a61.000000,61.000000,47
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fchpf 
is the cutoff frequency in Hz for case 2.}}
.EQN 5 -14 542 0 0
{0:fphpf}NAME:3.5
.TXT 0 14 543 0 0
Cg a59.000000,59.000000,55
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fphpf 
is the passband cutoff frequency in Hz for case 1}}
.EQN 4 -14 544 0 0
{0:fshpf}NAME:2.5
.TXT 0 14 545 0 0
Cg a59.000000,59.000000,65
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fshpf 
is the stopband cutoff frequency in Hz (fs < fp) for case 1}}
.EQN 5 -14 1182 0 0
{0:\qchpf}NAME:2*{0:\p}NAME*{0:fchpf}NAME*{0:Ts}NAME
.EQN 0 17 1183 0 0
{0:\qphpf}NAME:2*{0:\p}NAME*{0:fphpf}NAME*{0:Ts}NAME
.EQN 0 18 1184 0 0
{0:\qshpf}NAME:2*{0:\p}NAME*{0:fshpf}NAME*{0:Ts}NAME
.EQN 4 -35 1185 0 0
{0:\wchpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qchpf}NAME)/(2)),2*{0:\p}NAME*{0:fchpf}NAME)
.EQN 0 49 1808 0 0
{0:\qphpf}NAME={0}?_n_u_l_l_
.EQN 4 0 1809 0 0
{0:\qshpf}NAME={0}?_n_u_l_l_
.EQN 2 -49 1186 0 0
{0:\wphpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qphpf}NAME)/(2)),2*{0:\p}NAME*{0:fphpf}NAME)
.EQN 2 49 1810 0 0
{0:\wphpf}NAME={0}?_n_u_l_l_
.EQN 4 -49 1187 0 0
{0:\wshpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\qshpf}NAME)/(2)),2*{0:\p}NAME*{0:fshpf}NAME)
.EQN 0 49 1811 0 0
{0:\wshpf}NAME={0}?_n_u_l_l_
.TXT 8 -49 546 0 0
Cg a73.000000,73.000000,35
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Specifications for bandpass filter.}}
.EQN 5 0 547 0 0
{0:fcbpf}NAME:1.5
.TXT 0 14 548 0 0
Cg a61.000000,61.000000,63
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fcbpf 
is the center frequency in Hz in the passband for case 2.}}
.EQN 4 -14 553 0 0
{0:bwbpf}NAME:1
.TXT 0 14 554 0 0
Cg a61.000000,61.000000,50
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 bwbpf 
is the bandwidth of the passband for case 2.}}
.EQN 4 -14 549 0 0
{0:f1bpf}NAME:1.5
.TXT 0 14 550 0 0
Cg a59.000000,59.000000,87
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f1bpf 
is the lower passband cutoff frequency in Hz (f3bpf < f1bpf < f2bpf)
\par  for case 1.}}
.EQN 6 -14 551 0 0
{0:f2bpf}NAME:2.5
.TXT 0 14 552 0 0
Cg a59.000000,59.000000,87
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f2bpf 
is the upper passband cutoff frequency in Hz (f1bpf < f2bpf < f4bpf) 
\par for case 1.}}
.EQN 6 -14 555 0 0
{0:f3bpf}NAME:1
.TXT 0 14 556 0 0
Cg a59.000000,59.000000,78
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f3bpf 
is the lower stopband cutoff frequency in Hz (f3bpf < f1bpf) for case 1.}}
.EQN 5 -14 557 0 0
{0:f4bpf}NAME:3
.TXT 0 14 558 0 0
Cg a59.000000,59.000000,78
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f4bpf 
is the upper stopband cutoff frequency in Hz (f2bpf < f4bpf) for case 1.}}
.EQN 4 -14 1912 0 0
{0:f1bpf}NAME:{0:if}NAME({0:case}NAME÷2,{0:fcbpf}NAME-({0:bwbpf}NAME)/(2),{0:f1bpf}NAME)
.EQN 0 32 1913 0 0
{0:f2bpf}NAME:{0:if}NAME({0:case}NAME÷2,{0:fcbpf}NAME+({0:bwbpf}NAME)/(2),{0:f2bpf}NAME)
.EQN 4 -32 1914 0 0
{0:\q1bpf}NAME:2*{0:\p}NAME*{0:f1bpf}NAME*{0:Ts}NAME
.EQN 0 17 1915 0 0
{0:\q2bpf}NAME:2*{0:\p}NAME*{0:f2bpf}NAME*{0:Ts}NAME
.EQN 0 18 1916 0 0
{0:\q3bpf}NAME:2*{0:\p}NAME*{0:f3bpf}NAME*{0:Ts}NAME
.EQN 0 18 1917 0 0
{0:\q4bpf}NAME:2*{0:\p}NAME*{0:f4bpf}NAME*{0:Ts}NAME
.EQN 5 -53 1922 0 0
{0:\q1bpf}NAME={0}?_n_u_l_l_
.EQN 0 14 1923 0 0
{0:\q2bpf}NAME={0}?_n_u_l_l_
.EQN 0 14 1924 0 0
{0:\q3bpf}NAME={0}?_n_u_l_l_
.EQN 0 15 1925 0 0
{0:\q4bpf}NAME={0}?_n_u_l_l_
.EQN 5 -43 1191 0 0
{0:\w1bpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q1bpf}NAME)/(2)),2*{0:\p}NAME*{0:f1bpf}NAME)
.EQN 7 0 1192 0 0
{0:\w2bpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q2bpf}NAME)/(2)),2*{0:\p}NAME*{0:f2bpf}NAME)
.EQN 6 0 1193 0 0
{0:\w3bpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q3bpf}NAME)/(2)),2*{0:\p}NAME*{0:f3bpf}NAME)
.EQN 6 0 1195 0 0
{0:\w4bpf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q4bpf}NAME)/(2)),2*{0:\p}NAME*{0:f4bpf}NAME)
.EQN 7 0 584 0 0
{0:\w4bpf}NAME:{0:if}NAME({0:\w1bpf}NAME*{0:\w2bpf}NAME<{0:\w3bpf}NAME*{0:\w4bpf}NAME,({0:\w1bpf}NAME*{0:\w2bpf}NAME)/({0:\w3bpf}NAME),{0:\w4bpf}NAME)
.EQN 7 0 585 0 0
{0:\w3bpf}NAME:{0:if}NAME({0:\w1bpf}NAME*{0:\w2bpf}NAME>{0:\w3bpf}NAME*{0:\w4bpf}NAME,({0:\w1bpf}NAME*{0:\w2bpf}NAME)/({0:\w4bpf}NAME),{0:\w3bpf}NAME)
.EQN 6 0 1934 0 0
{0:\w1bpf}NAME={0}?_n_u_l_l_
.EQN 0 14 1935 0 0
{0:\w2bpf}NAME={0}?_n_u_l_l_
.EQN 0 14 1936 0 0
{0:\w3bpf}NAME={0}?_n_u_l_l_
.EQN 0 15 1937 0 0
{0:\w4bpf}NAME={0}?_n_u_l_l_
.TXT 5 -43 559 0 0
Cg a73.000000,73.000000,35
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Specifications for bandstop filter.}}
.EQN 5 0 560 0 0
{0:fcbsf}NAME:2000
.TXT 0 14 561 0 0
Cg a61.000000,61.000000,63
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 fcbsf 
is the center frequency in Hz in the stopband for case 2.}}
.EQN 4 -14 562 0 0
{0:bwbsf}NAME:1000
.TXT 0 14 563 0 0
Cg a61.000000,61.000000,56
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 bwbsf 
is the bandwidth of the stopband in Hz for case 2.}}
.EQN 4 -14 564 0 0
{0:f1bsf}NAME:1500
.TXT 0 14 565 0 0
Cg a59.000000,59.000000,79
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f1bsf 
is the lower passband cutoff frequency in Hz (f1bsf < f3bsf)  for case 1.}}
.EQN 4 -14 566 0 0
{0:f2bsf}NAME:4000
.TXT 0 14 567 0 0
Cg a59.000000,59.000000,78
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f2bsf 
is the upper passband cutoff frequency in Hz (f4bsf < f2bsf) for case 1.}}
.EQN 4 -14 568 0 0
{0:f3bsf}NAME:2000
.TXT 0 14 569 0 0
Cg a59.000000,59.000000,87
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f3bsf 
is the lower stopband cutoff frequency in Hz (f1bsf < f3bsf < f4bsf) 
\par for case 1.}}
.EQN 5 -14 570 0 0
{0:f4bsf}NAME:3000
.TXT 0 14 571 0 0
Cg a59.000000,59.000000,87
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 f4bsf 
is the upper stopband cutoff frequency in Hz (f3bsf < f4bsf < f2bsf) 
\par for case 1.}}
.EQN 7 -14 1029 0 0
{0:f1bsf}NAME:{0:if}NAME({0:case}NAME÷2,{0:fcbsf}NAME-({0:bwbsf}NAME)/(2),{0:f1bsf}NAME)
.EQN 0 32 1030 0 0
{0:f2bsf}NAME:{0:if}NAME({0:case}NAME÷2,{0:fcbsf}NAME+({0:bwbsf}NAME)/(2),{0:f2bsf}NAME)
.EQN 6 -32 1196 0 0
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.EQN 0 17 1197 0 0
{0:\q2bsf}NAME:2*{0:\p}NAME*{0:f2bsf}NAME*{0:Ts}NAME
.EQN 0 18 1198 0 0
{0:\q3bsf}NAME:2*{0:\p}NAME*{0:f3bsf}NAME*{0:Ts}NAME
.EQN 0 18 1199 0 0
{0:\q4bsf}NAME:2*{0:\p}NAME*{0:f4bsf}NAME*{0:Ts}NAME
.EQN 7 -53 1826 0 0
{0:\w1bsf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q1bsf}NAME)/(2)),2*{0:\p}NAME*{0:f1bsf}NAME)
.EQN 3 45 1827 0 0
{0:\w1bsf}NAME={0}?_n_u_l_l_
.EQN 4 -45 1828 0 0
{0:\w2bsf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q2bsf}NAME)/(2)),2*{0:\p}NAME*{0:f2bsf}NAME)
.EQN 0 45 1829 0 0
{0:\w2bsf}NAME={0}?_n_u_l_l_
.EQN 11 -45 1202 0 0
{0:\w3bsf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q3bsf}NAME)/(2)),2*{0:\p}NAME*{0:f3bsf}NAME)
.EQN 2 45 1212 0 0
{0:\w3bsf}NAME={0}?_n_u_l_l_
.EQN 4 -45 1203 0 0
{0:\w4bsf}NAME:{0:if}NAME(({0:analog}NAME÷2)*({0:iit}NAME÷2),2*{0:fs}NAME*{0:tan}NAME(({0:\q4bsf}NAME)/(2)),2*{0:\p}NAME*{0:f4bsf}NAME)
.EQN 3 45 1213 0 0
{0:\w4bsf}NAME={0}?_n_u_l_l_
.EQN 4 -45 1204 0 0
{0:\w4bsf}NAME:{0:if}NAME({0:\w1bsf}NAME*{0:\w2bsf}NAME>{0:\w3bsf}NAME*{0:\w4bsf}NAME,({0:\w1bsf}NAME*{0:\w2bsf}NAME)/({0:\w3bsf}NAME),{0:\w4bsf}NAME)
.EQN 3 45 1214 0 0
{0:\w4bsf}NAME={0}?_n_u_l_l_
.EQN 4 -45 1205 0 0
{0:\w3bsf}NAME:{0:if}NAME({0:\w1bsf}NAME*{0:\w2bsf}NAME<{0:\w3bsf}NAME*{0:\w4bsf}NAME,({0:\w1bsf}NAME*{0:\w2bsf}NAME)/({0:\w4bsf}NAME),{0:\w3bsf}NAME)
.EQN 3 46 1215 0 0
{0:\w3bsf}NAME={0}?_n_u_l_l_
.TXT 3 -46 168 0 0
Cg a46.000000,46.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
CALCULATING THE ORDER N1}{\cf2   }}
.TXT 4 0 599 0 0
Cg a73.000000,73.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 N1 is 
the order of the filter for case 1.}}
.TXT 5 0 576 0 0
Cg a66.000000,66.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Order 
for lowpass filter.}}
.EQN 8 0 167 0 0
{0:N1}NAME:{0:if}NAME(({0:ap}NAME÷1)*({0:type}NAME÷1)*({0:case}NAME÷1),{0:ceil}NAME(({0:log}NAME(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1)))/(2*{0:log}NAME(({0:\wslpf}NAME)/({0:\wplpf}NAME)))),1)
.EQN 1 53 377 0 0
{0:N1}NAME={0}?_n_u_l_l_
.EQN 13 -53 743 0 0
{0:N1}NAME:{0:if}NAME((({0:ap}NAME÷2)+({0:ap}NAME÷3))*({0:type}NAME÷1)*({0:case}NAME÷1),{0:ceil}NAME(({0:acosh}NAME(\(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1))))/({0:acosh}NAME(({0:\wslpf}NAME)/({0:\wplpf}NAME)))),{0:N1}NAME)
.EQN 0 62 744 0 0
{0:N1}NAME={0}?_n_u_l_l_
.TXT 9 -62 794 0 0
Cg a72.000000,72.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Order 
for elliptic filter.}}
.EQN 5 0 768 0 0
{0:\wo2}NAME:\({0:\wplpf}NAME*{0:\wslpf}NAME)
.EQN 0 18 1788 0 0
{0:amax}NAME:{0:if}NAME({0:case}NAME÷2,3,{0:amax}NAME)
.EQN 4 -18 769 0 0
{0:k}NAME:{0:if}NAME({0:type}NAME÷1,({0:\wplpf}NAME)/({0:\wslpf}NAME),{0:if}NAME({0:type}NAME÷2,({0:\wshpf}NAME)/({0:\wphpf}NAME),{0:if}NAME({0:type}NAME÷3,({0:\w2bpf}NAME-{0:\w1bpf}NAME)/({0:\w4bpf}NAME-{0:\w3bpf}NAME),({0:\w4bsf}NAME-{0:\w3bsf}NAME)/(
{0:\w2bsf}NAME-{0:\w1bsf}NAME))))
.EQN 13 0 770 0 0
{0:\Wp}NAME:\({0:k}NAME)
.EQN 0 10 1790 0 0
{0:k}NAME:{0:if}NAME({0:case}NAME÷2,1,{0:k}NAME)
.EQN 4 -10 771 0 0
{0:\Ws}NAME:(1)/(\({0:k}NAME))
.EQN 0 10 772 0 0
{0:\Wc}NAME:1
.EQN 8 -10 1830 0 0
{0:kp}NAME:\(1-({0:k}NAME)^(2))
.EQN 4 0 774 0 0
{0:qo}NAME:(1)/(2)*(1-\({0:kp}NAME))/(1+\({0:kp}NAME))
.EQN 6 0 775 0 0
{0:q}NAME:{0:qo}NAME+2*({0:qo}NAME)^(5)+15*({0:qo}NAME)^(9)+150*({0:qo}NAME)^(13)
.EQN 0 33 1883 0 0
{0:q}NAME={0}?_n_u_l_l_
.EQN 4 -33 776 0 0
{0:D}NAME:((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1)
.EQN 0 27 1884 0 0
{0:D}NAME={0}?_n_u_l_l_
.EQN 6 -27 777 0 0
{0:N1}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:case}NAME÷1),{0:ceil}NAME(({0:log}NAME(16*{0:D}NAME))/({0:log}NAME((1)/({0:q}NAME)))),{0:N1}NAME)
.EQN 0 41 789 0 0
{0:N1}NAME={0}?_n_u_l_l_
.TXT 9 -41 577 0 0
Cg a66.000000,66.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Order 
for highpass filter.}}
.EQN 9 0 574 0 0
{0:N1}NAME:{0:if}NAME(({0:ap}NAME÷1)*({0:type}NAME÷2)*({0:case}NAME÷1),{0:ceil}NAME(({0:log}NAME(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1)))/(2*{0:log}NAME(({0:\wphpf}NAME)/({0:\wshpf}NAME)))),{0:N1}NAME)
.EQN 0 51 575 0 0
{0:N1}NAME={0}?_n_u_l_l_
.EQN 15 -51 757 0 0
{0:N1}NAME:{0:if}NAME((({0:ap}NAME÷2)+({0:ap}NAME÷3))*({0:type}NAME÷2)*({0:case}NAME÷1),{0:ceil}NAME(({0:acosh}NAME(\(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1))))/({0:acosh}NAME(({0:\wphpf}NAME)/({0:\wshpf}NAME)))),{0:N1}NAME)
.EQN 0 62 758 0 0
{0:N1}NAME={0}?_n_u_l_l_
.TXT 9 -62 578 0 0
Cg a66.000000,66.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Order 
for bandpass filter.}}
.EQN 9 1 579 0 0
{0:N1}NAME:{0:if}NAME(({0:type}NAME÷3)*({0:ap}NAME÷1)*({0:case}NAME÷1),{0:ceil}NAME(({0:log}NAME(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1)))/(2*{0:log}NAME(({0:\w4bpf}NAME-{0:\w3bpf}NAME)/({0:\w2bpf}NAME-{0:\w1bpf}NAME)))),{0:N1}NAME)
.EQN 0 53 580 0 0
{0:N1}NAME={0}?_n_u_l_l_
.EQN 20 -54 759 0 0
{0:N1}NAME:{0:if}NAME((({0:ap}NAME÷2)+({0:ap}NAME÷3))*({0:type}NAME÷3)*({0:case}NAME÷1),{0:ceil}NAME(({0:acosh}NAME(\(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1))))/({0:acosh}NAME(({0:\w4bpf}NAME-{0:\w3bpf}NAME)/({0:\w2bpf}NAME-{0:\w1bpf}NAME)
))),{0:N1}NAME)
.EQN 0 62 763 0 0
{0:N1}NAME={0}?_n_u_l_l_
.TXT 10 -62 581 0 0
Cg a66.000000,66.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Order 
for bandstop filter.}}
.EQN 9 1 582 0 0
{0:N1}NAME:{0:if}NAME(({0:type}NAME÷4)*({0:ap}NAME÷1)*({0:case}NAME÷1),{0:ceil}NAME(({0:log}NAME(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1)))/(2*{0:log}NAME(({0:\w2bsf}NAME-{0:\w1bsf}NAME)/({0:\w4bsf}NAME-{0:\w3bsf}NAME)))),{0:N1}NAME)
.EQN 0 57 583 0 0
{0:N1}NAME={0}?_n_u_l_l_
.EQN 14 -58 764 0 0
{0:N1}NAME:{0:if}NAME((({0:ap}NAME÷2)+({0:ap}NAME÷3))*({0:type}NAME÷4)*({0:case}NAME÷1),{0:ceil}NAME(({0:acosh}NAME(\(((10)^(0.1*{0:amin}NAME)-1)/((10)^(0.1*{0:amax}NAME)-1))))/({0:acosh}NAME(({0:\w2bsf}NAME-{0:\w1bsf}NAME)/({0:\w4bsf}NAME-{0:\w3bsf}NAME)
))),{0:N1}NAME)
.EQN 0 61 767 0 0
{0:N1}NAME={0}?_n_u_l_l_
.TXT 12 -60 588 0 0
Cg a72.000000,72.000000,94
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}{\f1\fcharset2\fnil Symbol;}}\plain
\cf1\fs20 \pard {\cf2 Calculating }{\cf2\f1 W}{\cf2 o.  }{\cf2\f1 W}{
\cf2 o is the half-power frequency for the Butterworth normalized 
lowpass filter.}}
.EQN 5 0 589 0 0
{0:\Wo}NAME:{0:if}NAME({0:ap}NAME÷1,(1)/((((10)^(0.1*{0:amax}NAME)-1))^((1)/(2*{0:N1}NAME))),1)
.EQN 0 30 1812 0 0
{0:\Wo}NAME={0}?_n_u_l_l_
.TXT 9 -30 595 0 0
Cg a72.000000,72.000000,34
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Selecting the order of the filter.}}
.EQN 4 0 520 0 0
{0:N}NAME:{0:if}NAME({0:case}NAME÷1,{0:N1}NAME,{0:N2}NAME)
.EQN 0 22 524 0 0
{0:N}NAME={0}?_n_u_l_l_
.TXT 0 17 521 0 0
Cg a46.000000,46.000000,29
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 N is 
the order of the filter.}}
.TXT 5 -39 598 0 0
Cg a72.000000,72.000000,58
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
CALCULATING THE NORMALIZED LOWPASS POLE AND ZERO LOCATIONS}}
.EQN 5 -1 16 0 0
{0:REM}NAME:{0:mod}NAME({0:N}NAME,2)
.TXT 0 14 17 0 0
Cg a59.000000,59.000000,112
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 REM is 
the remainder when N is divided by 2.  If REM is 1, the order N is 
odd.  If REM = 0, the order N is even.}}
.TXT 6 -14 22 0 0
Cg a59.000000,59.000000,63
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 s}{\cf2
\fs16\dn 1}{\cf2 , s}{\cf2\fs16\dn 2}{\cf2 , ....., s}{\cf2\fs16\dn N}{
\cf2  are normalized analog lowpass pole locations.}}
.TXT 4 0 805 0 0
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\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculation of normalized lowpass pole locations for Butterworth filter.}}
.EQN 9 0 20 0 0
({0:s}NAME)[(1):{0:if}NAME({0:REM}NAME÷1,-1,0)
.EQN 5 0 132 0 0
{0:min}NAME:{0:if}NAME({0:REM}NAME÷1,({0:N}NAME+1)/(2),({0:N}NAME)/(2)+1)
.EQN 0 28 133 0 0
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.EQN 0 22 398 0 0
{0:max}NAME:{0:if}NAME({0:N}NAME÷1,1,{0:max}NAME)
.EQN 5 -50 1817 0 0
{0:m}NAME:{0:min}NAME;{0:max}NAME
.EQN 0 15 1818 0 0
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.EQN 6 -15 1819 0 0
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.EQN 7 0 136 0 0
{0:maxa}NAME:{0:if}NAME({0:REM}NAME÷1,({0:N}NAME-1)/(2),({0:N}NAME)/(2))
.EQN 0 24 400 0 0
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.EQN 6 -24 26 0 0
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.EQN 0 13 138 0 0
{0:evena}NAME:{0:if}NAME({0:REM}NAME÷1,0,1)
.EQN 5 -13 27 0 0
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.EQN 0 28 28 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculation of normalized lowpass pole locations for Chebyshev and 
Inverse Chevyshev filter.}}
.EQN 5 0 806 0 0
{0:a}NAME:{0:if}NAME({0:ap}NAME÷2,(1)/({0:N}NAME)*{0:asinh}NAME((1)/(\((10)^(0.1*{0:amax}NAME)-1))),{0:if}NAME({0:ap}NAME÷3,(1)/({0:N}NAME)*{0:asinh}NAME(\((10)^(0.1*{0:amin}NAME)-1)),1))
.EQN 7 0 811 0 0
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.EQN 0 26 826 0 0
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.EQN 5 -26 808 0 0
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.EQN 0 26 894 0 0
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.EQN 6 -26 809 0 0
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.EQN 4 0 810 0 0
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.EQN 6 0 812 0 0
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.EQN 6 0 813 0 0
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.EQN 6 0 814 0 0
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.EQN 10 0 1813 0 0
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.EQN 8 0 1814 0 0
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.EQN 5 0 1815 0 0
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.EQN 8 0 1816 0 0
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.TXT 10 0 840 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculation of normalized lowpass pole locations for elliptic filter.}}
.EQN 6 0 841 0 0
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.EQN 13 0 842 0 0
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.EQN 14 0 843 0 0
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.EQN 8 0 844 0 0
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.EQN 0 23 845 0 0
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.EQN 0 11 846 0 0
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.EQN 7 -34 847 0 0
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.EQN 6 0 848 0 0
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.EQN 22 0 849 0 0
({0:\W}NAME)[({0:i}NAME):(2*({0:q}NAME)^(0.25)*((0,50,{0:m}NAME,(((-1))^({0:m}NAME)*({0:q}NAME)^({0:m}NAME*({0:m}NAME+1))*{0:sin}NAME((2*{0:m}NAME+1)*{0:\p}NAME*({0:i}NAME-{0:muminus}NAME)/({0:N}NAME)))){64}))/(1+2*((1,50,{0:m}NAME,(((-1))^({0:m}NAME)*(
{0:q}NAME)^((({0:m}NAME)^(2)))*{0:cos}NAME(2*{0:m}NAME*{0:\p}NAME*({0:i}NAME-{0:muminus}NAME)/({0:N}NAME)))){64}))
.EQN 0 56 850 0 0
({0:\W}NAME)[({0:i}NAME)={0}?_n_u_l_l_
.EQN 13 -56 851 0 0
({0:V}NAME)[({0:i}NAME):\((1-{0:k}NAME*((({0:\W}NAME)[({0:i}NAME)))^(2))*(1-(((({0:\W}NAME)[({0:i}NAME)))^(2))/({0:k}NAME)))
.EQN 1 34 852 0 0
({0:\W}NAME)[({0:i}NAME):{0:if}NAME({0:N}NAME÷1,(10)^(-50),({0:\W}NAME)[({0:i}NAME))
.EQN 4 -34 1831 0 0
({0:Ao}NAME)[({0:i}NAME):(1)/(((({0:\W}NAME)[({0:i}NAME)))^(2))
.EQN 11 0 855 0 0
({0:Bo}NAME)[({0:i}NAME):((({0:\so}NAME*({0:V}NAME)[({0:i}NAME)))^(2)+((({0:\W}NAME)[({0:i}NAME)*{0:W}NAME))^(2))/(((1+({0:\so}NAME)^(2)*((({0:\W}NAME)[({0:i}NAME)))^(2)))^(2))
.EQN 11 0 856 0 0
({0:B1}NAME)[({0:i}NAME):(2*{0:\so}NAME*({0:V}NAME)[({0:i}NAME))/(1+({0:\so}NAME)^(2)*((({0:\W}NAME)[({0:i}NAME)))^(2))
.EQN 2 40 854 0 0
({0:Ao}NAME)[({0:i}NAME){18999}={0}?_n_u_l_l_
.EQN 0 11 963 0 0
({0:Bo}NAME)[({0:i}NAME){18999}={0}?_n_u_l_l_
.EQN 0 12 964 0 0
({0:B1}NAME)[({0:i}NAME){18999}={0}?_n_u_l_l_
.EQN 8 -63 857 0 0
{0:Ho}NAME:{0:if}NAME({0:REM}NAME÷1,{0:\so}NAME*((1,{0:r}NAME,{0:i}NAME,(({0:Bo}NAME)[({0:i}NAME))/(({0:Ao}NAME)[({0:i}NAME))){65}),(10)^(-0.05*{0:amax}NAME)*((1,{0:r}NAME,{0:i}NAME,(({0:Bo}NAME)[({0:i}NAME))/(({0:Ao}NAME)[({0:i}NAME))){65}))
.TXT 12 0 858 0 0
Cg a59.000000,59.000000,63
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 s}{\cf2
\fs16\dn 1}{\cf2 , s}{\cf2\fs16\dn 2}{\cf2 , ....., s}{\cf2\fs16\dn N}{
\cf2  are normalized analog lowpass pole locations.}}
.EQN 4 0 859 0 0
({0:se}NAME)[(1):{0:if}NAME({0:REM}NAME÷1,-{0:\so}NAME,0)
.TXT 0 23 860 0 0
Cg a54.000000,54.000000,63
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 If N 
is odd, there is a normalized analog pole at s = -sinh(a).}}
.EQN 4 -13 861 0 0
({0:se}NAME)[(1)={0}?_n_u_l_l_
.EQN 6 -10 862 0 0
({0:se}NAME)[(2*{0:i}NAME):{0:if}NAME(({0:REM}NAME÷1)*(((({0:B1}NAME)[({0:i}NAME)))^(2)̣4*({0:Bo}NAME)[({0:i}NAME)),-((({0:B1}NAME)[({0:i}NAME))/(2))+0.5*\(((({0:B1}NAME)[({0:i}NAME)))^(2)-4*({0:Bo}NAME)[({0:i}NAME)),0)
.EQN 8 0 863 0 0
({0:se}NAME)[(2*{0:i}NAME+1):{0:if}NAME(({0:REM}NAME÷1)*(((({0:B1}NAME)[({0:i}NAME)))^(2)̣4*({0:Bo}NAME)[({0:i}NAME)),-((({0:B1}NAME)[({0:i}NAME))/(2))-0.5*\(((({0:B1}NAME)[({0:i}NAME)))^(2)-4*({0:Bo}NAME)[({0:i}NAME)),0)
.EQN 15 0 864 0 0
({0:se}NAME)[(2*{0:i}NAME):{0:if}NAME(({0:REM}NAME÷1)*(((({0:B1}NAME)[({0:i}NAME)))^(2)<(4*({0:Bo}NAME)[({0:i}NAME))),-((({0:B1}NAME)[({0:i}NAME))/(2))+1j*0.5*\(-((({0:B1}NAME)[({0:i}NAME)))^(2)+4*({0:Bo}NAME)[({0:i}NAME)),({0:se}NAME)[(2*{0:i}NAME))
.EQN 6 0 865 0 0
({0:se}NAME)[(2*{0:i}NAME+1):{0:if}NAME(({0:REM}NAME÷1)*(((({0:B1}NAME)[({0:i}NAME)))^(2)<(4*({0:Bo}NAME)[({0:i}NAME))),(({0:se}NAME)[(2*{0:i}NAME))],({0:se}NAME)[(2*{0:i}NAME+1))
.EQN 6 0 867 0 0
({0:se}NAME)[(2*{0:i}NAME-1):{0:if}NAME(({0:REM}NAME÷0)*(((({0:B1}NAME)[({0:i}NAME)))^((2))>(4*({0:Bo}NAME)[({0:i}NAME))),-((({0:B1}NAME)[({0:i}NAME))/(2))+0.5*\(((({0:B1}NAME)[({0:i}NAME)))^(2)-4*({0:Bo}NAME)[({0:i}NAME)),({0:se}NAME)[(2*{0:i}NAME-1))
.EQN 6 0 868 0 0
({0:se}NAME)[(2*{0:i}NAME):{0:if}NAME(({0:REM}NAME÷0)*(((({0:B1}NAME)[({0:i}NAME)))^(2)>4*({0:Bo}NAME)[({0:i}NAME)),-((({0:B1}NAME)[({0:i}NAME))/(2))-0.5*\(((({0:B1}NAME)[({0:i}NAME)))^(2)-4*({0:Bo}NAME)[({0:i}NAME)),({0:se}NAME)[(2*{0:i}NAME))
.EQN 6 0 1832 0 0
({0:se}NAME)[(2*{0:i}NAME-1):{0:if}NAME(({0:REM}NAME÷0)*(((({0:B1}NAME)[({0:i}NAME)))^(2)<(4*({0:Bo}NAME)[({0:i}NAME))),-((({0:B1}NAME)[({0:i}NAME))/(2))+1j*0.5*\(-((({0:B1}NAME)[({0:i}NAME)))^(2)+4*({0:Bo}NAME)[({0:i}NAME)),({0:se}NAME)[(2*{0:i}NAME-1))
.EQN 7 0 870 0 0
({0:se}NAME)[(2*{0:i}NAME):{0:if}NAME(({0:REM}NAME÷0)*(((({0:B1}NAME)[({0:i}NAME)))^(2)<(4*({0:Bo}NAME)[({0:i}NAME))),(({0:se}NAME)[(2*{0:i}NAME-1))],({0:se}NAME)[(2*{0:i}NAME))
.EQN 5 0 872 0 0
({0:se}NAME)[(1):{0:if}NAME({0:N}NAME÷1,-{0:\so}NAME,({0:se}NAME)[(1))
.TXT 5 0 916 0 0
Cg a67.000000,67.000000,93
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculation of zero locations for normalized lowpass Butterworth 
filter and Chevyshev filter.}}
.EQN 4 0 917 0 0
{0:k}NAME:1;{0:N}NAME
.EQN 4 0 918 0 0
({0:szb}NAME)[({0:k}NAME):(10)^(50)
.EQN 0 12 919 0 0
({0:szc}NAME)[({0:k}NAME):(10)^(50)
.TXT 6 -12 831 0 0
Cg a67.000000,67.000000,78
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculation of zero locations for normalized lowpass inverse Chevyshev filter.
}}
.EQN 4 0 834 0 0
({0:szic}NAME)[(2*{0:i}NAME-1):1j*{0:sec}NAME({0:\p}NAME*(2*{0:i}NAME-1)/(2*{0:N}NAME))
.EQN 0 23 915 0 0
({0:szic}NAME)[(1):{0:if}NAME({0:N}NAME÷1,(10)^(50),({0:szic}NAME)[(1))
.EQN 6 -23 835 0 0
({0:szic}NAME)[(2*{0:i}NAME):(({0:szic}NAME)[(2*{0:i}NAME-1))]
.EQN 0 16 914 0 0
({0:szic}NAME)[({0:N}NAME):{0:if}NAME({0:REM}NAME÷1,(10)^(50),({0:szic}NAME)[({0:N}NAME))
.TXT 6 -16 899 0 0
Cg a73.000000,73.000000,70
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Calculating the zero locations for normalized lowpass elliptic filter.}}
.EQN 5 0 901 0 0
({0:sze}NAME)[(2*{0:i}NAME-1):1j*\(({0:Ao}NAME)[({0:i}NAME))
.EQN 5 0 902 0 0
({0:sze}NAME)[(2*{0:i}NAME):(({0:sze}NAME)[(2*{0:i}NAME-1))]
.EQN 5 0 907 0 0
({0:sze}NAME)[(1):{0:if}NAME({0:N}NAME÷1,(10)^(50),({0:sze}NAME)[(1))
.EQN 8 0 913 0 0
({0:sze}NAME)[({0:N}NAME):{0:if}NAME({0:REM}NAME÷1,(10)^(50),({0:sze}NAME)[({0:N}NAME))
.TXT 7 0 928 0 0
Cg a73.000000,73.000000,47
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Creating a single variable for poles and zeros.}}
.EQN 6 0 30 0 0
{0:k}NAME:1;{0:N}NAME
.EQN 4 0 815 0 0
({0:s}NAME)[({0:k}NAME):{0:if}NAME({0:ap}NAME÷1,({0:s}NAME)[({0:k}NAME),{0:if}NAME({0:ap}NAME÷2,({0:sc}NAME)[({0:k}NAME),{0:if}NAME({0:ap}NAME÷3,({0:sic}NAME)[({0:k}NAME),({0:se}NAME)[({0:k}NAME))))
.EQN 4 0 920 0 0
({0:sz}NAME)[({0:k}NAME):{0:if}NAME({0:ap}NAME÷1,({0:szb}NAME)[({0:k}NAME),{0:if}NAME({0:ap}NAME÷2,({0:szc}NAME)[({0:k}NAME),{0:if}NAME({0:ap}NAME÷3,({0:szic}NAME)[({0:k}NAME),({0:sze}NAME)[({0:k}NAME))))
.EQN 20 0 1833 0 0
({0:s}NAME)[({0:k}NAME){19002}={0}?_n_u_l_l_
.EQN 0 27 1834 0 0
-2*{0:Re}NAME(({0:s}NAME)[({0:k}NAME)){19002}={0}?_n_u_l_l_
.EQN 0 18 1835 0 0
((|(({0:s}NAME)[({0:k}NAME))))^(2){19002}={0}?_n_u_l_l_
.EQN 23 -45 921 0 0
({0:sz}NAME)[({0:k}NAME)={0}?_n_u_l_l_
.EQN 29 1 925 0 0
{0:NoZ}NAME:{0:if}NAME({0:REM}NAME÷1,{0:N}NAME-1,{0:N}NAME)
.EQN 0 22 926 0 0
{0:NoZ}NAME:{0:if}NAME({0:N}NAME÷1,1,{0:NoZ}NAME)
.EQN 0 19 927 0 0
{0:k1}NAME:1;{0:NoZ}NAME
.TXT 4 -42 223 0 0
Cg a72.000000,72.000000,65
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Normalized analog pole-zero plot.  There are N zeros at infinity.}}
.EQN 5 1 226 0 0
{0:x}NAME:-1,-0.99;1
.EQN 0 14 227 0 0
{0:ty}NAME({0:x}NAME):\(1-({0:x}NAME)^(2))
.EQN 0 15 228 0 0
{0:by}NAME({0:x}NAME):-\(1-({0:x}NAME)^(2))
.EQN 2 -22 224 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Im}NAME(({0:s}NAME)[({0:k}NAME)),{0:ty}NAME({0:x}NAME),{0:by}NAME({0:x}NAME)@1&-1&(_n_u_l_l_&_n_u_l_l_)&{0:Re}NAME(({0:s}NAME)[({0:k}NAME)),{0:x}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 0 6 0 1 1 NO-TRACE-STRING
0 1 6 0 1 1 NO-TRACE-STRING
0 1 6 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 25 22 10 0 3 Pole Locations
.EQN 32 0 839 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Im}NAME(({0:s}NAME)[({0:k}NAME)),{0:Im}NAME(({0:sz}NAME)[({0:k1}NAME)),{0:ty}NAME({0:x}NAME),{0:by}NAME({0:x}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:Re}NAME(({0:s}NAME)[({0:k}NAME)),{0:Re}NAME(({0:sz}NAME)[({0:k1}NAME)),{0:x}NAME,
{0:x}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 0 0 0 1 1 NO-TRACE-STRING
4 0 1 0 1 1 NO-TRACE-STRING
0 1 2 0 1 1 NO-TRACE-STRING
0 1 2 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 25 22 10 0 3 Pole-Zero Plot
.TXT 42 -8 241 0 0
Cg a72.000000,72.000000,55
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Normalized analog lowpass magnitude and phase response.}}
.EQN 7 0 473 0 0
{0:NoPpD}NAME:200
.TXT 0 11 474 0 0
Cg a62.000000,62.000000,51
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 NoPpD 
is the number of frequency points per decade.}}
.EQN 4 -11 475 0 0
{0:\wstart}NAME:0.01
.TXT 0 14 476 0 0
Cg a58.000000,58.000000,46
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 wstart 
is the starting frequency in radians/s.}}
.EQN 8 -14 477 0 0
{0:\wend}NAME:(10)^(7)
.TXT 0 14 478 0 0
Cg a59.000000,59.000000,42
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 wend 
is the ending frequency in radians/s.}}
.EQN 4 -14 479 0 0
{0:NoD}NAME:{0:ceil}NAME({0:log}NAME(({0:\wend}NAME)/({0:\wstart}NAME)))
.TXT 0 22 480 0 0
Cg a55.000000,55.000000,29
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 NoD is 
the number of decades.}}
.EQN 6 -22 481 0 0
{0:NoP}NAME:{0:NoPpD}NAME*{0:NoD}NAME
.EQN 0 17 482 0 0
{0:i}NAME:0;{0:NoP}NAME
.EQN 0 12 483 0 0
({0:\w}NAME)[({0:i}NAME):(10)^({0:log}NAME({0:\wstart}NAME)+({0:i}NAME)/({0:NoPpD}NAME))
.EQN 7 -29 929 0 0
{0:Kc}NAME:{0:if}NAME(({0:ap}NAME÷2)*({0:REM}NAME÷1),((1,{0:N}NAME,{0:k}NAME,|(({0:s}NAME)[({0:k}NAME))){65}),{0:if}NAME(({0:ap}NAME÷2)*({0:REM}NAME÷0),(10)^(-0.05*{0:amax}NAME)*((1,{0:N}NAME,{0:k}NAME,|(({0:s}NAME)[({0:k}NAME))){65}),1))
.EQN 13 0 930 0 0
{0:Kc}NAME:{0:if}NAME(({0:ap}NAME÷3)*({0:N}NAME÷1),|(({0:s}NAME)[(1)),{0:if}NAME(({0:ap}NAME÷3)*({0:N}NAME>1),(((1,{0:N}NAME,{0:k}NAME,|(({0:s}NAME)[({0:k}NAME))){65}))/(((1,{0:NoZ}NAME,{0:k1}NAME,|(({0:sz}NAME)[({0:k1}NAME))){65})),{0:Kc}NAME))
.EQN 12 0 953 0 0
{0:Kc}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:N}NAME÷1),|(({0:s}NAME)[(1)),{0:if}NAME(({0:ap}NAME÷4)*({0:N}NAME>1),{0:Ho}NAME,{0:Kc}NAME))
.EQN 3 55 946 0 0
{0:Kc}NAME={0}?_n_u_l_l_
.EQN 6 -55 243 0 0
({0:Hna}NAME)[({0:i}NAME):({0:Kc}NAME)/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:s}NAME)[({0:k}NAME))){65}))
.EQN 14 1 958 0 0
({0:Hna}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:N}NAME÷1),({0:Kc}NAME)/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:s}NAME)[({0:k}NAME))){65})),({0:Hna}NAME)[({0:i}NAME))
.EQN 18 -1 943 0 0
({0:Hna}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:N}NAME>1),(((1,{0:NoZ}NAME,{0:k1}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:sz}NAME)[({0:k1}NAME))){65})*{0:Kc}NAME)/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:s}NAME)[(
{0:k}NAME))){65})),({0:Hna}NAME)[({0:i}NAME))
.EQN 0 58 819 0 0
|(({0:Hna}NAME)[(0))={0}?_n_u_l_l_
.EQN 14 -58 244 0 0
&&(_n_u_l_l_&_n_u_l_l_)&|(({0:Hna}NAME)[({0:i}NAME))@&&(_n_u_l_l_&_n_u_l_l_)&({0:\w}NAME)[({0:i}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 48 15 10 0 3 Mag Response (LIN) of Normalized LPF 
.EQN 26 0 1837 0 0
({0:dBna}NAME)[({0:i}NAME):{0:if}NAME(({0:Hna}NAME)[({0:i}NAME)÷0,-200,20*{0:log}NAME(|(({0:Hna}NAME)[({0:i}NAME))))
.EQN 2 0 1838 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:dBna}NAME)[({0:i}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&({0:\w}NAME)[({0:i}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 47 15 10 0 3 Mag Response (dB) of Normalized LPF 
.EQN 32 1 392 0 0
({0:dBna}NAME)[({0:NoPpD}NAME*{0:log}NAME((1)/({0:\wstart}NAME)))={0}?_n_u_l_l_
.EQN 8 2 248 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:arg}NAME(({0:Hna}NAME)[({0:i}NAME))@&&(_n_u_l_l_&_n_u_l_l_)&({0:\w}NAME)[({0:i}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 48 15 10 0 3 Phase Response of Normalized LPF 
.TXT 33 -3 259 0 0
Cg a73.000000,73.000000,219
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
denominator and numerator polynomial of the normalized analog lowpass 
transfer \par function Hna(s) expressed as the product of the 
second-order terms s}{\cf2\fs16\up 2}{\cf2  + a}{\cf2\fs16\dn 1}{\cf2 
s + a}{\cf2\fs16\dn 2}{\cf2 . \par If N is odd, there is one 
first-order term s + a}{\cf2\fs16\dn 2}{\cf2 .  }}
.EQN 9 1 260 0 0
({0:ab}NAME)[(0,0):0
.EQN 0 12 261 0 0
({0:ab}NAME)[(0,1):1
.EQN 0 12 262 0 0
({0:ab}NAME)[(0,2):-({0:s}NAME)[(1)
.EQN 5 -24 263 0 0
{0:start}NAME:{0:if}NAME({0:REM}NAME÷1,1,0)
.EQN 0 20 406 0 0
{0:start}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:start}NAME)
.EQN 4 -20 264 0 0
{0:end}NAME:{0:if}NAME({0:REM}NAME÷1,({0:N}NAME-1)/(2),({0:N}NAME)/(2)-1)
.EQN 0 25 401 0 0
{0:end}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:end}NAME)
.EQN 5 -25 265 0 0
{0:evena}NAME:{0:if}NAME({0:REM}NAME÷1,0,1)
.EQN 3 0 266 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 4 0 268 0 0
({0:ab}NAME)[({0:m}NAME,0):{0:if}NAME({0:N}NAME÷1,0,1)
.EQN 6 0 269 0 0
({0:ab}NAME)[({0:m}NAME,1):{0:if}NAME({0:N}NAME÷1,1,-2*{0:Re}NAME(({0:s}NAME)[(2*{0:m}NAME+{0:evena}NAME)))
.EQN 6 0 270 0 0
({0:ab}NAME)[({0:m}NAME,2):{0:if}NAME({0:N}NAME÷1,-({0:s}NAME)[(1),((|(({0:s}NAME)[(2*{0:m}NAME+{0:evena}NAME))))^(2))
.EQN 10 0 404 0 0
{0:ab}NAME={19002}?_n_u_l_l_
.TXT 13 -1 980 0 0
Cg a72.000000,72.000000,7
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 Q value}}
.EQN 4 1 981 0 0
({0:Q}NAME)[({0:m}NAME):(1)/(({0:ab}NAME)[({0:m}NAME,1))
.EQN 7 -1 982 0 0
({0:Q}NAME)[({0:m}NAME)={0}?_n_u_l_l_
.TXT 20 0 968 0 0
Cg a73.000000,73.000000,112
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Numerator polynomial of the inverse Chebyshev filter expressed as a 
product of second-order terms\par s}{\cf2\fs16\up 2}{\cf2  + b}{\cf2
\fs16\dn 1}{\cf2 s + b}{\cf2\fs16\dn 2}{\cf2 .}}
.EQN 5 0 972 0 0
{0:i1}NAME:0;{0:r}NAME-1
.EQN 3 0 969 0 0
({0:bb}NAME)[({0:i1}NAME,0):{0:if}NAME({0:ap}NAME÷3,1,0)
.EQN 3 0 970 0 0
({0:bb}NAME)[({0:i1}NAME,1):0
.EQN 4 0 971 0 0
({0:bb}NAME)[({0:i1}NAME,2):{0:if}NAME({0:ap}NAME÷3,((|(({0:szic}NAME)[(2*({0:i1}NAME+1)-1))))^(2),0)
.EQN 9 0 973 0 0
{0:bb}NAME={0}?_n_u_l_l_
.TXT 14 0 974 0 0
Cg a73.000000,73.000000,103
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Numerator polynomial of the elliptic filter expressed as a product of 
second-order terms\par s}{\cf2\fs16\up 2}{\cf2  + b}{\cf2\fs16\dn 1}{
\cf2 s + b}{\cf2\fs16\dn 2}{\cf2 .}}
.EQN 6 0 976 0 0
({0:bb}NAME)[({0:i1}NAME,0):{0:if}NAME({0:ap}NAME÷4,1,({0:bb}NAME)[({0:i1}NAME,0))
.EQN 4 0 977 0 0
({0:bb}NAME)[({0:i1}NAME,1):0
.EQN 5 0 978 0 0
({0:bb}NAME)[({0:i1}NAME,2):{0:if}NAME({0:ap}NAME÷4,((|(({0:sze}NAME)[(2*({0:i1}NAME+1)-1))))^(2),({0:bb}NAME)[({0:i1}NAME,2))
.EQN 10 0 979 0 0
{0:bb}NAME={0}?_n_u_l_l_
.TXT 11 0 272 0 0
Cg a72.000000,72.000000,124
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
denominator polynomial of the normalized lowpass transfer function 
given by \par s}{\cf2\fs16\up N}{\cf2  + a}{\cf2\fs16\dn N-1}{\cf2 s}{
\cf2\fs16\up N-1}{\cf2  + a}{\cf2\fs16\dn N-2}{\cf2 s}{\cf2\fs16\up N-2}{
\cf2  + ..... +a}{\cf2\fs16\dn 1}{\cf2 s + 1. }}
.EQN 7 0 447 0 0
{0:NN}NAME:{0:if}NAME({0:REM}NAME÷1,{0:N}NAME+1,{0:N}NAME)
.EQN 5 0 273 0 0
{0:n}NAME:0;{0:NN}NAME
.EQN 0 12 274 0 0
{0:p}NAME:0;{0:NN}NAME
.EQN 0 16 465 0 0
{0:NN}NAME={0}?_n_u_l_l_
.EQN 0 8 466 0 0
{0:start}NAME={0}?_n_u_l_l_
.EQN 0 9 467 0 0
{0:end}NAME={0}?_n_u_l_l_
.EQN 4 -45 275 0 0
({0:ab}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:ab}NAME)[({0:m}NAME,{0:n}NAME))
.EQN 0 21 468 0 0
{0:start}NAME:{0:if}NAME(({0:REM}NAME÷0)*({0:N}NAME>2),{0:start}NAME+1,{0:start}NAME)
.EQN 5 -21 276 0 0
({0:ad}NAME)[(0,{0:n}NAME):({0:ab}NAME)[(0,{0:n}NAME)
.EQN 0 13 422 0 0
({0:ad}NAME)[(0,0):{0:if}NAME({0:N}NAME÷1,0,({0:ad}NAME)[(0,0))
.EQN 0 20 470 0 0
({0:ad}NAME)[(0,0)={0}?_n_u_l_l_
.EQN 0 10 471 0 0
({0:ad}NAME)[(0,1)={0}?_n_u_l_l_
.EQN 0 11 472 0 0
({0:ad}NAME)[(0,2)={0}?_n_u_l_l_
.EQN 6 -54 277 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 6 0 278 0 0
({0:ad}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME(({0:N}NAME÷1)+({0:N}NAME÷2),({0:ad}NAME)[(0,{0:n}NAME),((0,{0:n}NAME,{0:p}NAME,({0:ab}NAME)[({0:m}NAME,{0:p}NAME)*({0:ad}NAME)[({0:m}NAME-1,{0:n}NAME-{0:p}NAME)){64}))
.EQN 10 0 279 0 0
{0:ad}NAME={0}?_n_u_l_l_
.EQN 13 1 451 0 0
({0:apn}NAME)[({0:n}NAME):({0:ad}NAME)[({0:end}NAME,{0:n}NAME)
.EQN 22 2 281 0 0
{0:apn}NAME={0}?_n_u_l_l_
.TXT 19 -3 983 0 0
Cg a72.000000,72.000000,125
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
numerator polynomial of the normalized lowpass transfer function given 
by \par s}{\cf2\fs16\up 2r}{\cf2  + a}{\cf2\fs16\dn N-1}{\cf2 s}{\cf2
\fs16\up 2r}{\cf2\fs16\up -1}{\cf2  + a}{\cf2\fs16\dn N-2}{\cf2 s}{\cf2
\fs16\up 2r}{\cf2\fs16\up -2}{\cf2  + ..... +a}{\cf2\fs16\dn 1}{\cf2 s 
+ 1. }}
.EQN 12 0 985 0 0
{0:n}NAME:0;2*{0:r}NAME
.EQN 0 12 986 0 0
{0:p}NAME:0;2*{0:r}NAME
.EQN 0 16 1056 0 0
{0:r}NAME={0}?_n_u_l_l_
.EQN 4 -28 990 0 0
({0:bb}NAME)[({0:i1}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:bb}NAME)[({0:i1}NAME,{0:n}NAME))
.EQN 0 22 1010 0 0
{0:endn}NAME:{0:if}NAME({0:N}NAME<4,1,{0:r}NAME-1)
.EQN 5 -22 992 0 0
({0:bd}NAME)[(0,{0:n}NAME):({0:bb}NAME)[(0,{0:n}NAME)
.EQN 0 13 1003 0 0
{0:i1}NAME:1;{0:endn}NAME
.EQN 12 -13 998 0 0
({0:bd}NAME)[({0:i1}NAME,{0:n}NAME):{0:if}NAME(({0:N}NAME<4),({0:bd}NAME)[(0,{0:n}NAME),((0,{0:n}NAME,{0:p}NAME,({0:bb}NAME)[({0:i1}NAME,{0:p}NAME)*({0:bd}NAME)[({0:i1}NAME-1,{0:n}NAME-{0:p}NAME)){64}))
.EQN 15 0 999 0 0
{0:bd}NAME={0}?_n_u_l_l_
.EQN 13 1 1000 0 0
({0:bpn}NAME)[({0:n}NAME):({0:bd}NAME)[({0:endn}NAME,{0:n}NAME)
.EQN 22 2 1001 0 0
{0:bpn}NAME={0}?_n_u_l_l_
.TXT 32 -2 597 0 0
Cg a72.000000,72.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
FREQUENCY TRANSFORMED POLE-ZERO LOCATIONS}}
.TXT 5 -1 602 0 0
Cg a72.000000,72.000000,48
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Lowpass-to-lowpass pole and zero transformation.}}
.EQN 4 0 603 0 0
{0:\wolpf}NAME:{0:if}NAME({0:case}NAME÷1,{0:\Wo}NAME*{0:\wplpf}NAME,{0:\wclpf}NAME)
.EQN 6 0 1011 0 0
{0:\wolpf}NAME:{0:if}NAME(({0:ap}NAME÷3)*({0:case}NAME÷1),{0:\wslpf}NAME,{0:\wolpf}NAME)
.EQN 4 0 1012 0 0
{0:\wolpf}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:case}NAME÷1),\({0:\wplpf}NAME*{0:\wslpf}NAME),{0:\wolpf}NAME)
.EQN 4 0 610 0 0
({0:sfslp}NAME)[({0:k}NAME):{0:\wolpf}NAME*({0:s}NAME)[({0:k}NAME)
.EQN 0 17 1013 0 0
({0:szfslp}NAME)[({0:k}NAME):{0:\wolpf}NAME*({0:sz}NAME)[({0:k}NAME)
.EQN 4 -17 1474 0 0
({0:sfslp}NAME)[({0:k}NAME){19002}={0}?_n_u_l_l_
.EQN 0 29 1475 0 0
({0:szfslp}NAME)[({0:k}NAME){19002}={0}?_n_u_l_l_
.TXT 31 -29 1014 0 0
Cg a72.000000,72.000000,49
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Lowpass-to-highpass pole and zero transformation.}}
.EQN 5 0 1479 0 0
{0:\wohpf}NAME:{0:if}NAME({0:case}NAME÷1,({0:\wphpf}NAME)/({0:\Wo}NAME),({0:\wchpf}NAME)/({0:\Wo}NAME))
.EQN 6 0 1483 0 0
{0:\wohpf}NAME:{0:if}NAME(({0:ap}NAME÷3)*({0:case}NAME÷1),{0:\wshpf}NAME,{0:\wohpf}NAME)
.EQN 5 0 1484 0 0
{0:\wohpf}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:case}NAME÷1),\({0:\wphpf}NAME*{0:\wshpf}NAME),{0:\wohpf}NAME)
.EQN 7 0 1019 0 0
({0:sfshp}NAME)[({0:k}NAME):{0:if}NAME(({0:s}NAME)[({0:k}NAME)÷0,0,({0:\wohpf}NAME)/(({0:s}NAME)[({0:k}NAME)))
.EQN 0 25 1020 0 0
({0:szfshp}NAME)[({0:k}NAME):{0:if}NAME(({0:sz}NAME)[({0:k}NAME)÷0,0,({0:\wohpf}NAME)/(({0:sz}NAME)[({0:k}NAME)))
.EQN 7 -25 1476 0 0
({0:sfshp}NAME)[({0:k}NAME)={0}?_n_u_l_l_
.EQN 0 29 1477 0 0
({0:szfshp}NAME)[({0:k}NAME)={0}?_n_u_l_l_
.TXT 34 -29 1025 0 0
Cg a72.000000,72.000000,49
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Lowpass-to-bandpass pole and zero transformation.}}
.EQN 7 1 1680 0 0
{0:\Wo}NAME:{0:if}NAME(({0:ap}NAME÷3)*({0:type}NAME÷3)*({0:case}NAME÷1),({0:\w4bpf}NAME-{0:\w3bpf}NAME)/({0:\w2bpf}NAME-{0:\w1bpf}NAME),{0:\Wo}NAME)
.EQN 8 0 1677 0 0
{0:\Wo}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:type}NAME÷3)*({0:case}NAME÷1),\(({0:\w4bpf}NAME-{0:\w3bpf}NAME)/({0:\w2bpf}NAME-{0:\w1bpf}NAME)),{0:\Wo}NAME)
.EQN 6 0 618 0 0
({0:sbp}NAME)[({0:k}NAME):{0:\Wo}NAME*({0:s}NAME)[({0:k}NAME)
.EQN 7 0 619 0 0
({0:R1}NAME)[({0:k}NAME):{0:Re}NAME(({0:sbp}NAME)[({0:k}NAME))
.EQN 0 13 620 0 0
({0:I1}NAME)[({0:k}NAME):{0:Im}NAME(({0:sbp}NAME)[({0:k}NAME))
.EQN 0 13 621 0 0
({0:R2}NAME)[({0:k}NAME):((({0:R1}NAME)[({0:k}NAME)))^(2)
.EQN 0 12 622 0 0
({0:I2}NAME)[({0:k}NAME):((({0:I1}NAME)[({0:k}NAME)))^(2)
.EQN 6 -38 623 0 0
{0:\w21}NAME:({0:\w2bpf}NAME-{0:\w1bpf}NAME)/(2)
.EQN 6 0 624 0 0
({0:A}NAME)[({0:k}NAME):(4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+({0:I2}NAME)[({0:k}NAME)-({0:R2}NAME)[({0:k}NAME)
.EQN 12 -1 1249 0 0
({0:Ra}NAME)[({0:k}NAME):\((\(((({0:A}NAME)[({0:k}NAME)))^(2)+4*({0:R2}NAME)[({0:k}NAME)*({0:I2}NAME)[({0:k}NAME))-({0:A}NAME)[({0:k}NAME))/(2))
.EQN 0 26 1251 0 0
({0:Rb}NAME)[({0:k}NAME):\((\(((({0:A}NAME)[({0:k}NAME)))^(2)+4*({0:R2}NAME)[({0:k}NAME)*({0:I2}NAME)[({0:k}NAME))+({0:A}NAME)[({0:k}NAME))/(2))
.EQN 8 -26 625 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:I1}NAME)[({0:k}NAME)̣0,{0:\w21}NAME*(({0:R1}NAME)[({0:k}NAME)+({0:Ra}NAME)[({0:k}NAME))+1j*{0:\w21}NAME*(({0:I1}NAME)[({0:k}NAME)-({0:Rb}NAME)[({0:k}NAME)),0)
.EQN 6 0 626 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:I1}NAME)[({0:k}NAME)<0,{0:\w21}NAME*(({0:R1}NAME)[({0:k}NAME)-({0:Ra}NAME)[({0:k}NAME))+1j*{0:\w21}NAME*(-({0:I1}NAME)[({0:k}NAME)+({0:Rb}NAME)[({0:k}NAME)),({0:sfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 7 0 1553 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:I1}NAME)[({0:k}NAME)÷0,{0:\w21}NAME*({0:R1}NAME)[({0:k}NAME)+1j*{0:\w21}NAME*\((4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))-((({0:R1}NAME)[({0:k}NAME)))^(2)),({0:sfsbp}NAME)[(2*
{0:k}NAME-1))
.EQN 9 0 1554 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:R1}NAME)[({0:k}NAME)÷0)*(({0:I1}NAME)[({0:k}NAME)>0),1j*{0:\w21}NAME*(\((4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+((({0:I1}NAME)[({0:k}NAME)))^(2))-({0:I1}NAME)[({0:k}NAME)),(
{0:sfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 12 0 1559 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:R1}NAME)[({0:k}NAME)÷0)*(({0:I1}NAME)[({0:k}NAME)<0),1j*{0:\w21}NAME*(\((4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+((({0:I1}NAME)[({0:k}NAME)))^(2))-({0:I1}NAME)[({0:k}NAME)),(
{0:sfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 8 0 627 0 0
({0:sfsbp}NAME)[(2*{0:k}NAME):(({0:sfsbp}NAME)[(2*{0:k}NAME-1))]
.EQN 8 0 628 0 0
{0:m}NAME:1;2*{0:N}NAME
.EQN 4 0 629 0 0
({0:sfsbp}NAME)[({0:m}NAME)=
.EQN 41 0 1032 0 0
{0:k}NAME:1;{0:N}NAME
.EQN 4 0 1031 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):0
.EQN 0 16 1033 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME):(10)^(50)
.EQN 5 -16 1039 0 0
({0:szbp}NAME)[({0:k}NAME):{0:\Wo}NAME*({0:sz}NAME)[({0:k}NAME)
.EQN 5 0 1040 0 0
({0:Rz1}NAME)[({0:k}NAME):{0:Re}NAME(({0:szbp}NAME)[({0:k}NAME))
.EQN 0 13 1041 0 0
({0:Iz1}NAME)[({0:k}NAME):{0:Im}NAME(({0:szbp}NAME)[({0:k}NAME))
.EQN 0 13 1042 0 0
({0:Rz2}NAME)[({0:k}NAME):((({0:Rz1}NAME)[({0:k}NAME)))^(2)
.EQN 0 12 1043 0 0
({0:Iz2}NAME)[({0:k}NAME):((({0:Iz1}NAME)[({0:k}NAME)))^(2)
.EQN 6 -38 1044 0 0
{0:\w21}NAME:({0:\w2bpf}NAME-{0:\w1bpf}NAME)/(2)
.EQN 6 0 1045 0 0
({0:Az}NAME)[({0:k}NAME):(4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+({0:Iz2}NAME)[({0:k}NAME)-({0:Rz2}NAME)[({0:k}NAME)
.EQN 14 0 1239 0 0
({0:Raz}NAME)[({0:k}NAME):\((\(((({0:Az}NAME)[({0:k}NAME)))^(2)+4*({0:Rz2}NAME)[({0:k}NAME)*({0:Iz2}NAME)[({0:k}NAME))-({0:Az}NAME)[({0:k}NAME))/(2))
.EQN 0 29 1246 0 0
({0:Rbz}NAME)[({0:k}NAME):\((\(((({0:Az}NAME)[({0:k}NAME)))^(2)+4*({0:Rz2}NAME)[({0:k}NAME)*({0:Iz2}NAME)[({0:k}NAME))+({0:Az}NAME)[({0:k}NAME))/(2))
.EQN 6 -30 1046 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Iz1}NAME)[({0:k}NAME)̣0),{0:\w21}NAME*(({0:Rz1}NAME)[({0:k}NAME)+({0:Raz}NAME)[({0:k}NAME))+1j*{0:\w21}NAME*(({0:Iz1}NAME)[({0:k}NAME)-({0:Rbz}NAME)[({0:k}NAME)),(
{0:szfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 10 0 1047 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Iz1}NAME)[({0:k}NAME)<0),{0:\w21}NAME*(({0:Rz1}NAME)[({0:k}NAME)-({0:Raz}NAME)[({0:k}NAME))+1j*{0:\w21}NAME*(-({0:Iz1}NAME)[({0:k}NAME)+({0:Rbz}NAME)[({0:k}NAME)),(
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.EQN 10 1 1560 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:Rz1}NAME)[({0:k}NAME)÷0)*(({0:Iz1}NAME)[({0:k}NAME)>0),1j*{0:\w21}NAME*(\((4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+((({0:Iz1}NAME)[({0:k}NAME)))^(2))-({0:Iz1}NAME)[(
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.EQN 9 0 1561 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:Rz1}NAME)[({0:k}NAME)÷0)*(({0:Iz1}NAME)[({0:k}NAME)<0),1j*{0:\w21}NAME*(\((4*{0:\w1bpf}NAME*{0:\w2bpf}NAME)/((({0:\w2bpf}NAME-{0:\w1bpf}NAME))^(2))+((({0:Iz1}NAME)[({0:k}NAME)))^(2))-({0:Iz1}NAME)[(
{0:k}NAME)),({0:szfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 7 -1 1048 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME):(({0:szfsbp}NAME)[(2*{0:k}NAME-1))]
.EQN 0 20 1055 0 0
({0:szfsbp}NAME)[(2*{0:N}NAME-1):{0:if}NAME({0:REM}NAME÷1,0,({0:szfsbp}NAME)[(2*{0:N}NAME-1))
.EQN 5 -19 1068 0 0
({0:szfsbp}NAME)[(2*{0:N}NAME):{0:if}NAME({0:REM}NAME÷1,(10)^(50),({0:szfsbp}NAME)[(2*{0:N}NAME))
.EQN 5 0 1720 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:ap}NAME÷1)+({0:ap}NAME÷2),0,({0:szfsbp}NAME)[(2*{0:k}NAME-1))
.EQN 5 0 1721 0 0
({0:szfsbp}NAME)[(2*{0:k}NAME):{0:if}NAME(({0:ap}NAME÷1)+({0:ap}NAME÷2),(10)^(50),({0:szfsbp}NAME)[(2*{0:k}NAME))
.EQN 3 0 1049 0 0
{0:m}NAME:1;2*{0:N}NAME
.EQN 3 0 1050 0 0
({0:szfsbp}NAME)[({0:m}NAME)=
.TXT 52 0 613 0 0
Cg a34.875000,34.875000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Lowpass-to-bandstop pole-zero transformation.}}
.EQN 7 0 1683 0 0
{0:\Wo}NAME:{0:if}NAME(({0:ap}NAME÷3)*({0:type}NAME÷4),({0:\w2bsf}NAME-{0:\w1bsf}NAME)/({0:\w4bsf}NAME-{0:\w3bsf}NAME),{0:\Wo}NAME)
.EQN 10 0 1678 0 0
{0:\Wo}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:type}NAME÷4),\(({0:\w2bsf}NAME-{0:\w1bsf}NAME)/({0:\w4bsf}NAME-{0:\w3bsf}NAME)),{0:\Wo}NAME)
.EQN 7 0 639 0 0
({0:sbs}NAME)[({0:k}NAME):{0:\Wo}NAME*({0:s}NAME)[({0:k}NAME)
.EQN 6 0 640 0 0
({0:R1}NAME)[({0:k}NAME):{0:Re}NAME(({0:sbs}NAME)[({0:k}NAME))
.EQN 0 13 641 0 0
({0:I1}NAME)[({0:k}NAME):{0:Im}NAME(({0:sbs}NAME)[({0:k}NAME))
.EQN 0 13 642 0 0
({0:R2}NAME)[({0:k}NAME):((({0:R1}NAME)[({0:k}NAME)))^(2)
.EQN 0 12 643 0 0
({0:I2}NAME)[({0:k}NAME):((({0:I1}NAME)[({0:k}NAME)))^(2)
.EQN 6 -38 644 0 0
{0:\w21}NAME:({0:\w2bsf}NAME-{0:\w1bsf}NAME)/(2)
.EQN 0 18 645 0 0
({0:mag}NAME)[({0:k}NAME):({0:R2}NAME)[({0:k}NAME)+({0:I2}NAME)[({0:k}NAME)
.EQN 0 17 646 0 0
{0:\w2m1}NAME:{0:\w2bsf}NAME-{0:\w1bsf}NAME
.EQN 6 -35 647 0 0
({0:A}NAME)[({0:k}NAME):(({0:I2}NAME)[({0:k}NAME)-({0:R2}NAME)[({0:k}NAME))/(((({0:mag}NAME)[({0:k}NAME)))^(2))*({0:\w2m1}NAME)^(2)+4*{0:\w1bsf}NAME*{0:\w2bsf}NAME
.EQN 0 35 648 0 0
({0:B}NAME)[({0:k}NAME):(2*|(({0:R1}NAME)[({0:k}NAME))*|(({0:I1}NAME)[({0:k}NAME)))/(((({0:mag}NAME)[({0:k}NAME)))^(2))*({0:\w2m1}NAME)^(2)
.EQN 10 -35 1232 0 0
({0:RA}NAME)[({0:k}NAME):(1)/(2)*\((\(((({0:A}NAME)[({0:k}NAME)))^(2)+((({0:B}NAME)[({0:k}NAME)))^(2))-({0:A}NAME)[({0:k}NAME))/(2))
.EQN 0 26 1235 0 0
({0:RB}NAME)[({0:k}NAME):1j*(1)/(2)*(\((\(((({0:A}NAME)[({0:k}NAME)))^(2)+((({0:B}NAME)[({0:k}NAME)))^(2))+({0:A}NAME)[({0:k}NAME))/(2))-(({0:I1}NAME)[({0:k}NAME)*{0:\w2m1}NAME)/(({0:mag}NAME)[({0:k}NAME)))
.EQN 8 -26 649 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:I1}NAME)[({0:k}NAME)>0,{0:\w21}NAME*(({0:R1}NAME)[({0:k}NAME))/(({0:mag}NAME)[({0:k}NAME))+({0:RA}NAME)[({0:k}NAME)+({0:RB}NAME)[({0:k}NAME),0)
.EQN 10 0 650 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:I1}NAME)[({0:k}NAME)<0,({0:\w21}NAME*(({0:R1}NAME)[({0:k}NAME))/(({0:mag}NAME)[({0:k}NAME))-(1)/(2)*\((\(((({0:A}NAME)[({0:k}NAME)))^(2)+((({0:B}NAME)[({0:k}NAME)))^(2))-({0:A}NAME)[({0:k}NAME))/(2)))+(
{0:RB}NAME)[({0:k}NAME),({0:sfsbs}NAME)[(2*{0:k}NAME-1))
.EQN 9 -1 651 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME):(({0:sfsbs}NAME)[(2*{0:k}NAME-1))]
.EQN 7 1 1487 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:I1}NAME)[({0:k}NAME)÷0)*(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))^(2)̣4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:\w21}NAME)/(({0:R1}NAME)[({0:k}NAME))+(1)/(2)*\(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))
^(2)-4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:sfsbs}NAME)[(2*{0:k}NAME-1))
.EQN 8 0 1492 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME):{0:if}NAME((({0:I1}NAME)[({0:k}NAME)÷0)*(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))^(2)̣4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:\w21}NAME)/(({0:R1}NAME)[({0:k}NAME))-(1)/(2)*\(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))^(
2)-4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:sfsbs}NAME)[(2*{0:k}NAME))
.EQN 9 0 1514 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:I1}NAME)[({0:k}NAME)÷0)*(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))^(2)<4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:\w21}NAME)/(({0:R1}NAME)[({0:k}NAME))+1j*(1)/(2)*\(-((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME
))))^(2)+4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:sfsbs}NAME)[(2*{0:k}NAME-1))
.EQN 8 0 1515 0 0
({0:sfsbs}NAME)[(2*{0:k}NAME):{0:if}NAME((({0:I1}NAME)[({0:k}NAME)÷0)*(((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))))^(2)<4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:\w21}NAME)/(({0:R1}NAME)[({0:k}NAME))-1j*(1)/(2)*\(-((({0:\w2m1}NAME)/(({0:R1}NAME)[({0:k}NAME))
))^(2)+4*{0:\w1bsf}NAME*{0:\w2bsf}NAME),({0:sfsbs}NAME)[(2*{0:k}NAME))
.EQN 6 0 652 0 0
{0:m}NAME:1;2*{0:N}NAME
.EQN 3 0 653 0 0
({0:sfsbs}NAME)[({0:m}NAME)=
.EQN 58 0 1222 0 0
({0:sz}NAME)[({0:k}NAME):{0:\Wo}NAME*({0:sz}NAME)[({0:k}NAME)
.EQN 4 0 1085 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME-1):1j*\({0:\w1bsf}NAME*{0:\w2bsf}NAME)
.EQN 0 24 1094 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME):(({0:szfsbs}NAME)[(2*{0:k}NAME-1))]
.EQN 4 -24 1070 0 0
({0:Rz1}NAME)[({0:k}NAME):{0:Re}NAME(({0:sz}NAME)[({0:k}NAME))
.EQN 0 13 1071 0 0
({0:Iz1}NAME)[({0:k}NAME):{0:Im}NAME(({0:sz}NAME)[({0:k}NAME))
.EQN 0 13 1072 0 0
({0:Rz2}NAME)[({0:k}NAME):((({0:Rz1}NAME)[({0:k}NAME)))^(2)
.EQN 0 12 1073 0 0
({0:Iz2}NAME)[({0:k}NAME):((({0:Iz1}NAME)[({0:k}NAME)))^(2)
.EQN 6 -38 1074 0 0
{0:\w21}NAME:({0:\w2bsf}NAME-{0:\w1bsf}NAME)/(2)
.EQN 0 18 1075 0 0
({0:mag}NAME)[({0:k}NAME):({0:Rz2}NAME)[({0:k}NAME)+({0:Iz2}NAME)[({0:k}NAME)
.EQN 0 17 1076 0 0
{0:\w2m1}NAME:{0:\w2bsf}NAME-{0:\w1bsf}NAME
.EQN 6 -35 1077 0 0
({0:Az}NAME)[({0:k}NAME):(({0:Iz2}NAME)[({0:k}NAME)-({0:Rz2}NAME)[({0:k}NAME))/(((({0:mag}NAME)[({0:k}NAME)))^(2))*({0:\w2m1}NAME)^(2)+4*{0:\w1bsf}NAME*{0:\w2bsf}NAME
.EQN 0 35 1078 0 0
({0:Bz}NAME)[({0:k}NAME):(2*|(({0:Rz1}NAME)[({0:k}NAME))*|(({0:Iz1}NAME)[({0:k}NAME)))/(((({0:mag}NAME)[({0:k}NAME)))^(2))*({0:\w2m1}NAME)^(2)
.EQN 10 -35 1226 0 0
({0:RAz}NAME)[({0:k}NAME):(1)/(2)*\((\(((({0:Az}NAME)[({0:k}NAME)))^(2)+((({0:Bz}NAME)[({0:k}NAME)))^(2))-({0:Az}NAME)[({0:k}NAME))/(2))
.EQN 0 26 1230 0 0
({0:RBz}NAME)[({0:k}NAME):1j*(1)/(2)*(\((\(((({0:Az}NAME)[({0:k}NAME)))^(2)+((({0:Bz}NAME)[({0:k}NAME)))^(2))+({0:Az}NAME)[({0:k}NAME))/(2))-(({0:Iz1}NAME)[({0:k}NAME)*{0:\w2m1}NAME)/(({0:mag}NAME)[({0:k}NAME)))
.EQN 10 -26 1086 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Iz1}NAME)[({0:k}NAME)̣0),{0:\w21}NAME*(({0:Rz1}NAME)[({0:k}NAME))/(({0:mag}NAME)[({0:k}NAME))+({0:RAz}NAME)[({0:k}NAME)+({0:RBz}NAME)[({0:k}NAME),({0:szfsbs}NAME)[(2*
{0:k}NAME-1))
.EQN 9 0 1089 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Iz1}NAME)[({0:k}NAME)<0),({0:\w21}NAME*(({0:Rz1}NAME)[({0:k}NAME))/(({0:mag}NAME)[({0:k}NAME))-({0:RAz}NAME)[({0:k}NAME))+({0:RBz}NAME)[({0:k}NAME),({0:szfsbs}NAME)[(2*
{0:k}NAME-1))
.EQN 7 0 1081 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME):(({0:szfsbs}NAME)[(2*{0:k}NAME-1))]
.EQN 5 0 1543 0 0
({0:AAz}NAME)[({0:k}NAME):{0:if}NAME(({0:Iz1}NAME)[({0:k}NAME){56}0,((({0:\w2bsf}NAME-{0:\w1bsf}NAME)/(({0:Iz1}NAME)[({0:k}NAME))))^(2)+4*{0:\w1bsf}NAME*{0:\w2bsf}NAME,0)
.EQN 6 0 1540 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Rz1}NAME)[({0:k}NAME)÷0)*(({0:Iz1}NAME)[({0:k}NAME)>0),1j*(1)/(2)*(\(({0:AAz}NAME)[({0:k}NAME))-({0:\w2m1}NAME)/(({0:Iz1}NAME)[({0:k}NAME))),({0:szfsbs}NAME)[(2*{0:k}NAME-1))

.EQN 6 0 1551 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME-1):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*(({0:Rz1}NAME)[({0:k}NAME)÷0)*(({0:Iz1}NAME)[({0:k}NAME)<0),1j*(1)/(2)*(\(({0:AAz}NAME)[({0:k}NAME))-({0:\w2m1}NAME)/(({0:Iz1}NAME)[({0:k}NAME))),({0:szfsbs}NAME)[(2*{0:k}NAME-1))

.EQN 7 0 1542 0 0
({0:szfsbs}NAME)[(2*{0:k}NAME):(({0:szfsbs}NAME)[(2*{0:k}NAME-1))]
.EQN 19 1 1097 0 0
({0:szfsbs}NAME)[({0:m}NAME)=
.TXT 46 0 198 0 0
Cg a72.000000,72.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Frequency scaled analog pole-zero plot.  }}
.EQN 4 0 666 0 0
{0:Pend}NAME:{0:if}NAME(({0:type}NAME÷1)+({0:type}NAME÷2),{0:N}NAME,2*{0:N}NAME)
.EQN 4 0 667 0 0
{0:p}NAME:1;{0:Pend}NAME
.EQN 4 0 670 0 0
({0:sfs}NAME)[({0:p}NAME):{0:if}NAME({0:type}NAME÷1,({0:sfslp}NAME)[({0:p}NAME),{0:if}NAME({0:type}NAME÷2,({0:sfshp}NAME)[({0:p}NAME),{0:if}NAME({0:type}NAME÷3,({0:sfsbp}NAME)[({0:p}NAME),({0:sfsbs}NAME)[({0:p}NAME))))
.EQN 5 0 687 0 0
({0:szfs}NAME)[({0:p}NAME):{0:if}NAME({0:type}NAME÷1,({0:szfslp}NAME)[({0:p}NAME),{0:if}NAME({0:type}NAME÷2,({0:szfshp}NAME)[({0:p}NAME),{0:if}NAME({0:type}NAME÷3,({0:szfsbp}NAME)[({0:p}NAME),({0:szfsbs}NAME)[({0:p}NAME))))
.EQN 7 0 607 0 0
{0:\wo}NAME:{0:if}NAME({0:type}NAME÷1,{0:\wolpf}NAME,{0:if}NAME({0:type}NAME÷2,({0:\wohpf}NAME)/({0:\Wo}NAME),{0:if}NAME({0:type}NAME÷3,(\({0:\w1bpf}NAME*{0:\w2bpf}NAME))/({0:\Wo}NAME),(\({0:\w1bsf}NAME*{0:\w2bsf}NAME))/({0:\Wo}NAME))))
.EQN 6 0 230 0 0
{0:x}NAME:-{0:\wo}NAME,-0.99*{0:\wo}NAME;{0:\wo}NAME
.EQN 0 23 231 0 0
{0:ty}NAME({0:x}NAME):\(({0:\wo}NAME)^(2)-({0:x}NAME)^(2))
.EQN 0 15 232 0 0
{0:by}NAME({0:x}NAME):-\(({0:\wo}NAME)^(2)-({0:x}NAME)^(2))
.EQN 3 -38 724 0 0
{0:p2end}NAME:{0:if}NAME((({0:ap}NAME÷1)+({0:ap}NAME÷2))*({0:type}NAME÷3),{0:N}NAME,{0:Pend}NAME)
.EQN 5 0 1099 0 0
{0:p2end}NAME:{0:if}NAME(({0:REM}NAME÷1)*(({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:type}NAME÷1),{0:N}NAME-1,{0:p2end}NAME)
.EQN 5 0 1098 0 0
{0:p2end}NAME:{0:if}NAME(({0:REM}NAME÷1)*(({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:type}NAME÷3),2*{0:N}NAME-1,{0:p2end}NAME)
.EQN 4 0 725 0 0
{0:p2}NAME:1;{0:p2end}NAME
.EQN 6 7 199 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Im}NAME(({0:sfs}NAME)[({0:p}NAME)),{0:Im}NAME(({0:szfs}NAME)[({0:p2}NAME)),{0:ty}NAME({0:x}NAME),{0:by}NAME({0:x}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:Re}NAME(({0:sfs}NAME)[({0:p}NAME)),{0:Re}NAME(({0:szfs}NAME)[({0:p2}NAME)),
{0:x}NAME,{0:x}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 0 0 0 1 1 NO-TRACE-STRING
4 0 1 0 1 1 NO-TRACE-STRING
0 1 2 0 1 1 NO-TRACE-STRING
0 1 2 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 29 23 10 0 3 Analog Pole-Zero Diagram
.EQN 34 0 738 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Im}NAME(({0:sfs}NAME)[({0:p}NAME)),{0:ty}NAME({0:x}NAME),{0:by}NAME({0:x}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:Re}NAME(({0:sfs}NAME)[({0:p}NAME)),{0:x}NAME,{0:x}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 0 0 0 1 1 NO-TRACE-STRING
0 1 6 0 1 1 NO-TRACE-STRING
0 1 6 0 1 1 NO-TRACE-STRING
0 1 6 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 26 23 10 0 3 Analog Pole Locations
.TXT 37 -7 201 0 0
Cg a72.000000,72.000000,53
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Frequency scaled analog magnitude and phase response.}}
.EQN 10 -1 1100 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME({0:type}NAME÷1,(((1,{0:N}NAME,{0:k}NAME,|(({0:sfs}NAME)[({0:k}NAME))){65}))/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:sfs}NAME)[({0:k}NAME))){65})),1)
.EQN 12 0 1101 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME(({0:ap}NAME÷2)*({0:REM}NAME÷0)*({0:type}NAME÷1),(10)^(-0.05*{0:amax}NAME)*({0:Ha}NAME)[({0:i}NAME),({0:Ha}NAME)[({0:i}NAME))
.EQN 12 0 1102 0 0
{0:Kc}NAME:{0:if}NAME(({0:type}NAME÷4)+({0:ap}NAME÷3)+({0:ap}NAME÷4),(((1,{0:N}NAME,{0:k}NAME,|(({0:sfs}NAME)[({0:k}NAME))){65}))/(((1,{0:NoZ}NAME,{0:k1}NAME,|(({0:szfs}NAME)[({0:k1}NAME))){65})),1)
.EQN 13 0 1273 0 0
{0:Kc}NAME:{0:if}NAME({0:type}NAME÷2,1,{0:Kc}NAME)
.EQN 7 0 1103 0 0
{0:Kc}NAME:{0:if}NAME(({0:ap}NAME÷4)*({0:REM}NAME÷0),{0:Kc}NAME*(10)^(-0.05*{0:amax}NAME),{0:Kc}NAME)
.EQN 17 0 1104 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:N}NAME>1)*({0:type}NAME÷1),({0:Kc}NAME*((1,{0:NoZ}NAME,{0:k1}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:szfs}NAME)[({0:k1}NAME))){65}))/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[(
{0:i}NAME)-({0:sfs}NAME)[({0:k}NAME))){65})),({0:Ha}NAME)[({0:i}NAME))
.EQN 19 0 1110 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME({0:type}NAME÷2,(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME))){65}))/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:sfs}NAME)[({0:k}NAME))){65})),({0:Ha}NAME)[({0:i}NAME))
.EQN 12 0 1111 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME(({0:ap}NAME÷2)*({0:REM}NAME÷0),(10)^(-0.05*{0:amax}NAME)*({0:Ha}NAME)[({0:i}NAME),({0:Ha}NAME)[({0:i}NAME))
.EQN 11 0 1114 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:N}NAME>1)*({0:type}NAME÷2),({0:Kc}NAME*((1,{0:NoZ}NAME,{0:k1}NAME,(1j*({0:\w}NAME)[({0:i}NAME)-({0:szfs}NAME)[({0:k1}NAME))){65}))/(((1,{0:N}NAME,{0:k}NAME,(1j*({0:\w}NAME)[(
{0:i}NAME)-({0:sfs}NAME)[({0:k}NAME))){65})),({0:Ha}NAME)[({0:i}NAME))
.EQN 15 0 1272 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:N}NAME>1)*({0:REM}NAME÷1)*({0:type}NAME÷2),(1j*({0:\w}NAME)[({0:i}NAME))*({0:Ha}NAME)[({0:i}NAME),({0:Ha}NAME)[({0:i}NAME))
.EQN 15 0 1117 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME({0:type}NAME÷3,(((1,{0:N}NAME,{0:k}NAME,-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:k}NAME-1))*1j*({0:\w}NAME)[({0:i}NAME)){65}))/(((1,{0:N}NAME,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)-2*{0:Re}NAME(({0:sfs}NAME)[(2*
{0:k}NAME-1))*1j*({0:\w}NAME)[({0:i}NAME)+((|(({0:sfs}NAME)[(2*{0:k}NAME-1))))^(2))){65})),({0:Ha}NAME)[({0:i}NAME))
.EQN 19 0 1254 0 0
({0:Hb}NAME)[({0:i}NAME):{0:if}NAME(({0:type}NAME÷3)*(({0:ap}NAME÷3)+({0:ap}NAME÷4)),(((1,{0:N}NAME,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)+((|(({0:szfs}NAME)[(2*{0:k}NAME-1))))^(2))){65}))/(((1,{0:N}NAME,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)
-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:k}NAME-1))*1j*({0:\w}NAME)[({0:i}NAME)+((|(({0:sfs}NAME)[(2*{0:k}NAME-1))))^(2))){65})),1)
.EQN 14 0 1150 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:type}NAME÷3)*({0:REM}NAME÷0),({0:Hb}NAME)[({0:i}NAME),({0:Ha}NAME)[({0:i}NAME))
.EQN 13 0 1258 0 0
({0:Hc}NAME)[({0:i}NAME):{0:if}NAME(({0:type}NAME÷3)*(({0:ap}NAME÷3)+({0:ap}NAME÷4)),(((1,{0:N}NAME-1,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)+((|(({0:szfs}NAME)[(2*{0:k}NAME-1))))^(2))){65})*(-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:N}NAME-1))*1j*(
{0:\w}NAME)[({0:i}NAME)))/(((1,{0:N}NAME,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:k}NAME-1))*1j*({0:\w}NAME)[({0:i}NAME)+((|(({0:sfs}NAME)[(2*{0:k}NAME-1))))^(2))){65})),1)
.EQN 15 0 1157 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME((({0:ap}NAME÷3)+({0:ap}NAME÷4))*({0:type}NAME÷3)*({0:REM}NAME÷1)*({0:N}NAME>1),({0:Hc}NAME)[({0:i}NAME),({0:Ha}NAME)[({0:i}NAME))
.EQN 6 0 1520 0 0
({0:Resfs}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:type}NAME÷4)*(({0:I1}NAME)[({0:k}NAME)÷0),({0:sfs}NAME)[(2*{0:k}NAME-1)+({0:sfs}NAME)[(2*{0:k}NAME),{0:if}NAME(({0:type}NAME÷4)*(({0:I1}NAME)[({0:k}NAME){56}0),-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:k}NAME-1)),0)
)
.EQN 7 0 1524 0 0
({0:magsfs}NAME)[(2*{0:k}NAME-1):{0:if}NAME(({0:type}NAME÷4)*(({0:I1}NAME)[({0:k}NAME)÷0),({0:sfs}NAME)[(2*{0:k}NAME-1)*({0:sfs}NAME)[(2*{0:k}NAME),{0:if}NAME(({0:type}NAME÷4)*(({0:I1}NAME)[({0:k}NAME){56}0),((|(({0:sfs}NAME)[(2*{0:k}NAME-1))))^(2),0))
.EQN 13 0 691 0 0
({0:Ha}NAME)[({0:i}NAME):{0:if}NAME({0:type}NAME÷4,((1,{0:N}NAME,{0:k}NAME,(-((({0:\w}NAME)[({0:i}NAME)))^(2)+((|(({0:szfs}NAME)[(2*{0:k}NAME-1))))^(2))/((-((({0:\w}NAME)[({0:i}NAME)))^(2)+({0:Resfs}NAME)[(2*{0:k}NAME-1)*{0}1j*({0:\w}NAME)[({0:i}NAME))+(
{0:magsfs}NAME)[(2*{0:k}NAME-1))){65}),({0:Ha}NAME)[({0:i}NAME))
.EQN 11 0 730 0 0
{0:ka}NAME:1;{0:NoP}NAME
.EQN 5 0 728 0 0
({0:maxa}NAME)[(0):|(({0:Ha}NAME)[(0))
.EQN 0 13 732 0 0
({0:maxa}NAME)[({0:ka}NAME):{0:if}NAME(|(({0:Ha}NAME)[({0:ka}NAME))>({0:maxa}NAME)[({0:ka}NAME-1),|(({0:Ha}NAME)[({0:ka}NAME)),({0:maxa}NAME)[({0:ka}NAME-1))
.EQN 0 39 733 0 0
{0:maxb}NAME:({0:maxa}NAME)[({0:NoP}NAME)
.EQN 6 -52 734 0 0
({0:Ha}NAME)[({0:i}NAME):(({0:Ha}NAME)[({0:i}NAME))/({0:maxb}NAME)
.EQN 0 38 1662 0 0
{0:maxb}NAME={0}?_n_u_l_l_
.EQN 0 18 1663 0 0
(1)/({0:maxb}NAME)={0}?_n_u_l_l_
.EQN 4 -55 490 0 0
&&(_n_u_l_l_&_n_u_l_l_)&|(({0:Ha}NAME)[({0:i}NAME))@&&(_n_u_l_l_&_n_u_l_l_)&(({0:\w}NAME)[({0:i}NAME))/(2*{0:\p}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 48 15 10 0 3 Linear Magnitude Response
.EQN 30 -1 1637 0 0
{0:Nlp1}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\wplpf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1638 0 0
{0:Nlp2}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\wslpf}NAME)/({0:\wstart}NAME)))
.EQN 6 -28 1639 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nlp1}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1640 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nlp2}NAME)))={0}?_n_u_l_l_
.EQN 7 -31 1641 0 0
{0:Nhp1}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\wphpf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1642 0 0
{0:Nhp2}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\wshpf}NAME)/({0:\wstart}NAME)))
.EQN 6 -28 1643 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nhp1}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1644 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nhp2}NAME)))={0}?_n_u_l_l_
.EQN 6 -31 1619 0 0
{0:Nbp1}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w1bpf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1614 0 0
{0:Nbp2}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w2bpf}NAME)/({0:\wstart}NAME)))
.EQN 6 -28 1625 0 0
{0:Nbp3}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w3bpf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1626 0 0
{0:Nbp4}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w4bpf}NAME)/({0:\wstart}NAME)))
.EQN 9 -28 1603 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbp1}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1624 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbp2}NAME)))={0}?_n_u_l_l_
.EQN 4 -31 1627 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbp3}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1628 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbp4}NAME)))={0}?_n_u_l_l_
.EQN 5 -31 1656 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[(0)))={0}?_n_u_l_l_
.EQN 0 31 1657 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:NoP}NAME)))={0}?_n_u_l_l_
.EQN 6 -31 1629 0 0
{0:Nbs1}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w1bsf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1630 0 0
{0:Nbs2}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w2bsf}NAME)/({0:\wstart}NAME)))
.EQN 6 -28 1631 0 0
{0:Nbs3}NAME:{0:ceil}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w3bsf}NAME)/({0:\wstart}NAME)))
.EQN 0 28 1632 0 0
{0:Nbs4}NAME:{0:floor}NAME({0:NoPpD}NAME*{0:log}NAME(({0:\w4bsf}NAME)/({0:\wstart}NAME)))
.EQN 6 -28 1633 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbs1}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1634 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbs2}NAME)))={0}?_n_u_l_l_
.EQN 4 -31 1635 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbs3}NAME)))={0}?_n_u_l_l_
.EQN 0 31 1636 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:Nbs4}NAME)))={0}?_n_u_l_l_
.EQN 4 -31 1664 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[(0)))={0}?_n_u_l_l_
.EQN 0 31 1665 0 0
20*{0:log}NAME(|(({0:Ha}NAME)[({0:NoP}NAME)))={0}?_n_u_l_l_
.EQN 5 -31 491 0 0
({0:dBna}NAME)[({0:i}NAME):{0:if}NAME(({0:Ha}NAME)[({0:i}NAME)÷0,-200,20*{0:log}NAME(|(({0:Ha}NAME)[({0:i}NAME))))
.EQN 2 3 492 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:dBna}NAME)[({0:i}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&(({0:\w}NAME)[({0:i}NAME))/(2*{0:\p}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 47 15 10 0 3 Magnitude Response (dB) 
.EQN 26 1 495 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:arg}NAME(({0:Ha}NAME)[({0:i}NAME))@&&(_n_u_l_l_&_n_u_l_l_)&({0:\w}NAME)[({0:i}NAME)
1 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 48 15 10 0 3 Phase Response 
.TXT 36 -4 233 0 0
Cg a73.000000,73.000000,204
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Frequency transformed analog transfer function Ha(s) expressed as the 
product of the second-order terms s}{\cf2\fs16\up 2}{\cf2  + a}{\cf2
\fs16\dn 1}{\cf2 s + a}{\cf2\fs16\dn 2}{\cf2 .  aelh is for lowpass 
and highpass filters.  aeb is for bandpass and bandstop\par filters.}}
.TXT 8 3 707 0 0
Cg a70.000000,70.000000,71
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-order terms in the denominator for lowpass and highpass filters.}}
.EQN 4 -3 292 0 0
({0:aelh}NAME)[(0,0):0
.EQN 0 12 293 0 0
({0:aelh}NAME)[(0,1):1
.EQN 0 12 294 0 0
({0:aelh}NAME)[(0,2):-({0:sfs}NAME)[(1)
.EQN 5 -24 295 0 0
{0:start}NAME:{0:if}NAME({0:REM}NAME÷1,1,0)
.EQN 0 19 425 0 0
{0:start}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:start}NAME)
.EQN 4 -19 296 0 0
{0:end}NAME:{0:if}NAME({0:REM}NAME÷1,({0:N}NAME-1)/(2),({0:N}NAME)/(2)-1)
.EQN 0 24 424 0 0
{0:end}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:end}NAME)
.EQN 5 -24 297 0 0
{0:evena}NAME:{0:if}NAME({0:REM}NAME÷1,0,1)
.EQN 4 0 298 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 4 0 300 0 0
({0:aelh}NAME)[({0:m}NAME,0):{0:if}NAME({0:N}NAME÷1,0,1)
.EQN 4 0 301 0 0
({0:aelh}NAME)[({0:m}NAME,1):{0:if}NAME({0:N}NAME÷1,1,-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:m}NAME+{0:evena}NAME)))
.EQN 6 0 302 0 0
({0:aelh}NAME)[({0:m}NAME,2):{0:if}NAME({0:N}NAME÷1,1,((|(({0:sfs}NAME)[(2*{0:m}NAME+{0:evena}NAME))))^(2))
.EQN 11 2 1481 0 0
{0:aelh}NAME={150071}?_n_u_l_l_
.TXT 19 1 708 0 0
Cg a70.000000,70.000000,72
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-order terms in the denominator for bandpass and bandstop filters.}}
.EQN 4 -3 703 0 0
({0:aeb}NAME)[({0:k}NAME-1,0):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),1,0)
.EQN 4 0 704 0 0
({0:aeb}NAME)[({0:k}NAME-1,1):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),-2*{0:Re}NAME(({0:sfs}NAME)[(2*{0:k}NAME-1)),0)
.EQN 5 0 705 0 0
({0:aeb}NAME)[({0:k}NAME-1,2):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((|(({0:sfs}NAME)[(2*{0:k}NAME-1))))^(2),0)
.EQN 16 0 706 0 0
{0:aeb}NAME={0}?_n_u_l_l_
.TXT 17 1 282 0 0
Cg a72.000000,72.000000,138
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
denominator polynomial of the frequency scaled transfer function given 
by polynomial form \par s}{\cf2\fs16\up N}{\cf2  + a}{\cf2\fs16\dn N-1}{
\cf2 s}{\cf2\fs16\up N-1}{\cf2  + a}{\cf2\fs16\dn N-2}{\cf2 s}{\cf2\fs16
\up N-2}{\cf2  + ..... +a}{\cf2\fs16\dn 1}{\cf2 s + 1. }}
.TXT 7 0 709 0 0
Cg a72.000000,72.000000,56
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Denominator polynomial for lowpass and highpass filters.}}
.EQN 5 0 283 0 0
{0:n}NAME:0;{0:NN}NAME
.EQN 0 12 284 0 0
{0:p}NAME:0;{0:NN}NAME
.EQN 4 -12 285 0 0
({0:aelh}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:aelh}NAME)[({0:m}NAME,{0:n}NAME))
.EQN 5 0 286 0 0
({0:aflh}NAME)[(0,{0:n}NAME):({0:aelh}NAME)[(0,{0:n}NAME)
.EQN 0 13 434 0 0
({0:af}NAME)[(0,0):{0:if}NAME({0:N}NAME÷1,0,({0:aflh}NAME)[(0,0))
.EQN 0 20 469 0 0
{0:start}NAME:{0:if}NAME(({0:REM}NAME÷0)*({0:N}NAME>2),{0:start}NAME+1,{0:start}NAME)
.EQN 6 -33 287 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 6 0 288 0 0
({0:aflh}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME(({0:N}NAME÷1)+({0:N}NAME÷2),({0:aflh}NAME)[(0,{0:n}NAME),((0,{0:n}NAME,{0:p}NAME,({0:aelh}NAME)[({0:m}NAME,{0:p}NAME)*({0:aflh}NAME)[({0:m}NAME-1,{0:n}NAME-{0:p}NAME)){64}))
.EQN 14 2 289 0 0
{0:aflh}NAME={0}?_n_u_l_l_
.EQN 13 -1 290 0 0
({0:aps}NAME)[({0:n}NAME):({0:aflh}NAME)[({0:end}NAME,{0:n}NAME)
.EQN 20 1 291 0 0
{0:aps}NAME={0}?_n_u_l_l_
.TXT 21 -2 719 0 0
Cg a72.000000,72.000000,57
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Denominator polynomial for bandpass and bandstop filters.}}
.EQN 4 0 710 0 0
{0:n}NAME:0;2*{0:N}NAME
.EQN 0 12 711 0 0
{0:p}NAME:0;2*{0:N}NAME
.EQN 0 12 720 0 0
{0:k1}NAME:0;{0:N}NAME-1
.EQN 4 -24 712 0 0
({0:aeb}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:aeb}NAME)[({0:k1}NAME,{0:n}NAME))
.EQN 5 0 713 0 0
({0:afb}NAME)[(0,{0:n}NAME):({0:aeb}NAME)[(0,{0:n}NAME)
.EQN 6 0 714 0 0
{0:k1}NAME:1;{0:N}NAME-1
.EQN 6 0 715 0 0
({0:afb}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((0,{0:n}NAME,{0:p}NAME,({0:aeb}NAME)[({0:k1}NAME,{0:p}NAME)*({0:afb}NAME)[({0:k1}NAME-1,{0:n}NAME-{0:p}NAME)){64}),0)
.EQN 19 -1 716 0 0
{0:afb}NAME={150071}?_n_u_l_l_
.EQN 15 0 717 0 0
({0:apsb}NAME)[({0:n}NAME):({0:afb}NAME)[({0:N}NAME-1,{0:n}NAME)
.EQN 26 1 718 0 0
{0:apsb}NAME={150071}?_n_u_l_l_
.TXT 32 -1 1274 0 0
Cg a73.000000,73.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
TRANSFORMING ANALOG POLES AND ZEROS TO DIGITAL POLES AND ZEROS}}
.TXT 4 0 1275 0 0
Cg a63.000000,63.000000,82
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 iit = 
1 for impulse invariant transformation; iit = 2 for bilinear transformation.}}
.EQN 4 0 1335 0 0
{0:m}NAME:1;{0:Pend}NAME
.EQN 9 0 1277 0 0
({0:dp}NAME)[({0:m}NAME):{0:if}NAME({0:iit}NAME÷2,(1+({0:Ts}NAME)/(2)*({0:sfs}NAME)[({0:m}NAME))/(1-({0:Ts}NAME)/(2)*({0:sfs}NAME)[({0:m}NAME)),({0:e}NAME)^({0:Ts}NAME*({0:sfs}NAME)[({0:m}NAME)))
.EQN 9 0 1278 0 0
({0:dp}NAME)[({0:m}NAME){19002}=
.EQN 0 25 1279 0 0
|(({0:dp}NAME)[({0:m}NAME)){19002}=
.EQN 0 14 1280 0 0
{0:arg}NAME(({0:dp}NAME)[({0:m}NAME)){19002}=
.EQN 44 -39 1796 0 0
({0:szfs}NAME)[({0:m}NAME):{0:if}NAME(({0:iit}NAME÷1)*(({0:szfs}NAME)[({0:m}NAME)>(10)^(40)),-({0:szfs}NAME)[({0:m}NAME),({0:szfs}NAME)[({0:m}NAME))
.EQN 8 0 1336 0 0
({0:dz}NAME)[({0:m}NAME):{0:if}NAME({0:iit}NAME÷2,(1+({0:Ts}NAME)/(2)*({0:szfs}NAME)[({0:m}NAME))/(1-({0:Ts}NAME)/(2)*({0:szfs}NAME)[({0:m}NAME)),({0:e}NAME)^({0:Ts}NAME*({0:szfs}NAME)[({0:m}NAME)))
.EQN 4 37 1800 0 0
({0:pha}NAME)[({0:m}NAME):{0:if}NAME(({0:dz}NAME)[({0:m}NAME)÷0,0,{0:arg}NAME(({0:dz}NAME)[({0:m}NAME)))
.EQN 12 -37 1885 0 0
({0:dz}NAME)[({0:m}NAME){19002}=
.EQN 0 25 1886 0 0
|(({0:dz}NAME)[({0:m}NAME)){19002}=
.EQN 0 15 1887 0 0
({0:pha}NAME)[({0:m}NAME){19002}=
.EQN 59 -40 1285 0 0
{0:x}NAME:-1,-0.99;1
.EQN 0 14 1286 0 0
{0:ty}NAME({0:x}NAME):\(1-({0:x}NAME)^(2))
.EQN 0 20 1287 0 0
{0:by}NAME({0:x}NAME):-\(1-({0:x}NAME)^(2))
.EQN 3 -29 1288 0 0
2&-2&(_n_u_l_l_&_n_u_l_l_)&{0:Im}NAME(({0:dp}NAME)[({0:m}NAME)),{0:Im}NAME(({0:dz}NAME)[({0:m}NAME)),{0:ty}NAME({0:x}NAME),{0:by}NAME({0:x}NAME)@2&-2&(_n_u_l_l_&_n_u_l_l_)&{0:Re}NAME(({0:dp}NAME)[({0:m}NAME)),{0:Re}NAME(({0:dz}NAME)[({0:m}NAME)),{0:x}NAME

0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 0 0 0 1 1 NO-TRACE-STRING
5 0 1 0 1 1 NO-TRACE-STRING
0 1 3 0 1 1 NO-TRACE-STRING
0 1 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 19 10 0 3 Digital Pole-Zero Diagram
.EQN 40 -5 1341 0 0
{0:H}NAME({0:\q}NAME):(((1,{0:Pend}NAME,{0:m}NAME,(1-({0:dz}NAME)[({0:m}NAME)*({0:e}NAME)^(-1j*{0:\q}NAME))){65}))/(((1,{0:Pend}NAME,{0:m}NAME,(1-({0:dp}NAME)[({0:m}NAME)*({0:e}NAME)^(-1j*{0:\q}NAME))){65}))
.EQN 13 0 1578 0 0
{0:ka}NAME:1;{0:ceil}NAME((2*{0:\p}NAME)/(0.01))
.EQN 5 0 1579 0 0
({0:maxa}NAME)[(0):|({0:H}NAME(0))
.EQN 0 13 1580 0 0
({0:maxa}NAME)[({0:ka}NAME):{0:if}NAME(|({0:H}NAME({0:ka}NAME*0.01))>({0:maxa}NAME)[({0:ka}NAME-1),|({0:H}NAME({0:ka}NAME*0.01)),({0:maxa}NAME)[({0:ka}NAME-1))
.EQN 0 44 1581 0 0
{0:maxb}NAME:({0:maxa}NAME)[({0:ceil}NAME((2*{0:\p}NAME)/(0.01)))
.EQN 5 -57 1851 0 0
{0:maxb}NAME={0}?_n_u_l_l_
.EQN 0 17 1852 0 0
(1)/({0:maxb}NAME)={18999}?_n_u_l_l_
.EQN 5 -17 1866 0 0
{0:\q}NAME:0,0.01;2*{0:\p}NAME
.EQN 4 0 1868 0 0
&&(_n_u_l_l_&_n_u_l_l_)&|(({0:H}NAME({0:\q}NAME))/({0:maxb}NAME))@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\q}NAME)/(2*{0:\p}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 50 15 10 0 3 Mag Response (linear) of Digital Filter
.EQN 32 0 1870 0 0
{0:HdB}NAME({0:\q}NAME):{0:if}NAME({0:H}NAME({0:\q}NAME)÷0,-200,20*{0:log}NAME(|(({0:H}NAME({0:\q}NAME))/({0:maxb}NAME))))
.EQN 5 0 1871 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:HdB}NAME({0:\q}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&({0:\q}NAME)/(2*{0:\p}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 50 15 10 0 3 Mag Response (dB) of Digital Filter
.EQN 36 0 1872 0 0
{0:pha}NAME({0:\q}NAME):{0:if}NAME({0:H}NAME({0:\q}NAME)÷0,0,{0:arg}NAME({0:H}NAME({0:\q}NAME)))
.EQN 2 1 1873 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:pha}NAME({0:\q}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&({0:\q}NAME)/(2*{0:\p}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 6 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 50 15 10 0 3 Phase Response of Digital Filter
.EQN 31 -1 1695 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qplpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 24 1700 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qslpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 27 1701 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qclpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 5 -51 1702 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qphpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 28 1703 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qshpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 25 1704 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\qchpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 5 -53 1705 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q1bpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 25 1706 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q2bpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 24 1707 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q3bpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 5 -49 1875 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q4bpf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 5 0 1876 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q1bsf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 25 1878 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q2bsf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 6 -25 1882 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q3bsf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 0 30 1881 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\q4bsf}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.EQN 7 -30 1735 0 0
|(({0:H}NAME(0))/({0:maxb}NAME))={0}?_n_u_l_l_
.EQN 0 15 1736 0 0
{0:dB0}NAME:{0:if}NAME({0:H}NAME(0){56}0,20*{0:log}NAME(|(({0:H}NAME(0))/({0:maxb}NAME))),-1000)
.EQN 0 34 1737 0 0
{0:dB0}NAME={0}?_n_u_l_l_
.EQN 5 -49 1733 0 0
20*{0:log}NAME(|(({0:H}NAME({0:\p}NAME))/({0:maxb}NAME)))={0}?_n_u_l_l_
.TXT 5 0 1289 0 0
Cg a72.000000,72.000000,251
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Denominator and numerator polynomial of the transfer function as a 
product of second order polynomials.  The first column of the af 
matrix is 1, the second column is the coefficient to the\par z}{\cf2
\fs16\up -1}{\cf2  term, the third column is the coefficient to the z}{
\cf2\fs16\up -2}{\cf2  term.}}
.TXT 9 0 1352 0 0
Cg a73.000000,73.000000,137
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-Order Factors for Denominator Polynomial For Lowpass and 
Highpass Filters:\par Ignore the following for Bandpass and Bandstop Filters.}
}
.EQN 7 0 1353 0 0
({0:af}NAME)[(0,0):0
.EQN 0 12 1354 0 0
({0:af}NAME)[(0,1):1
.EQN 0 12 1355 0 0
({0:af}NAME)[(0,2):-({0:dp}NAME)[(1)
.EQN 5 -24 1356 0 0
{0:start}NAME:{0:if}NAME({0:REM}NAME÷1,1,0)
.EQN 0 20 1357 0 0
{0:start}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:start}NAME)
.EQN 4 -20 1358 0 0
{0:end}NAME:{0:if}NAME({0:REM}NAME÷1,({0:N}NAME-1)/(2),({0:N}NAME)/(2)-1)
.EQN 0 25 1359 0 0
{0:end}NAME:{0:if}NAME({0:N}NAME÷1,0,{0:end}NAME)
.EQN 5 -25 1360 0 0
{0:evena}NAME:{0:if}NAME({0:REM}NAME÷1,0,1)
.EQN 3 0 1361 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 4 0 1362 0 0
({0:af}NAME)[({0:m}NAME,0):{0:if}NAME({0:N}NAME÷1,0,1)
.EQN 6 0 1363 0 0
({0:af}NAME)[({0:m}NAME,1):{0:if}NAME({0:N}NAME÷1,1,-2*{0:Re}NAME(({0:dp}NAME)[(2*{0:m}NAME+{0:evena}NAME)))
.EQN 6 0 1364 0 0
({0:af}NAME)[({0:m}NAME,2):{0:if}NAME({0:N}NAME÷1,-({0:dp}NAME)[(1),((|(({0:dp}NAME)[(2*{0:m}NAME+{0:evena}NAME))))^(2))
.EQN 10 0 1365 0 0
{0:af}NAME={19002}?_n_u_l_l_
.TXT 22 0 1366 0 0
Cg a73.000000,73.000000,135
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-Order Factors for Numerator Polynomial For Lowpass and Highpass 
Filters:\par Ignore the following for Bandpass and Bandstop Filters.}}
.EQN 6 0 1367 0 0
({0:ag}NAME)[(0,0):0
.EQN 0 12 1368 0 0
({0:ag}NAME)[(0,1):1
.EQN 0 12 1369 0 0
({0:ag}NAME)[(0,2):-({0:dz}NAME)[({0:N}NAME)
.EQN 4 -24 1376 0 0
({0:ag}NAME)[({0:m}NAME,0):{0:if}NAME({0:N}NAME÷1,0,1)
.EQN 6 0 1377 0 0
({0:ag}NAME)[({0:m}NAME,1):{0:if}NAME({0:N}NAME÷1,1,-2*{0:Re}NAME(({0:dz}NAME)[(2*{0:m}NAME+{0:evena}NAME)))
.EQN 6 0 1378 0 0
({0:ag}NAME)[({0:m}NAME,2):{0:if}NAME({0:N}NAME÷1,-({0:dz}NAME)[(1),((|(({0:dz}NAME)[(2*{0:m}NAME+{0:evena}NAME))))^(2))
.EQN 10 0 1379 0 0
{0:ag}NAME={19002}?_n_u_l_l_
.TXT 18 0 1382 0 0
Cg a73.000000,73.000000,137
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-Order Factors for Denominator Polynomial For Bandpass and 
Bandstop Filters:\par Ignore the following for Lowpass and Highpass Filters.}}
.EQN 6 0 1396 0 0
{0:k}NAME:1;{0:N}NAME
.EQN 4 0 1397 0 0
({0:aff}NAME)[({0:k}NAME-1,0):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),1,0)
.EQN 5 0 1398 0 0
({0:aff}NAME)[({0:k}NAME-1,1):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),-2*{0:Re}NAME(({0:dp}NAME)[(2*{0:k}NAME-1)),0)
.EQN 5 0 1401 0 0
({0:aff}NAME)[({0:k}NAME-1,2):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((|(({0:dp}NAME)[(2*{0:k}NAME-1))))^(2),0)
.EQN 13 0 1402 0 0
{0:aff}NAME={150071}?_n_u_l_l_
.TXT 35 0 1403 0 0
Cg a73.000000,73.000000,135
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Second-Order Factors for Numerator Polynomial For Bandpass and 
Bandstop Filters:\par Ignore the following for Lowpass and Highpass Filters.}}
.EQN 6 0 1404 0 0
{0:k}NAME:1;{0:N}NAME
.EQN 4 0 1405 0 0
({0:agg}NAME)[({0:k}NAME-1,0):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),1,0)
.EQN 5 0 1406 0 0
({0:agg}NAME)[({0:k}NAME-1,1):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),-2*{0:Re}NAME(({0:dz}NAME)[(2*{0:k}NAME-1)),0)
.EQN 5 0 1407 0 0
({0:agg}NAME)[({0:k}NAME-1,2):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((|(({0:dz}NAME)[(2*{0:k}NAME-1))))^(2),0)
.EQN 5 0 1722 0 0
({0:agg}NAME)[({0:k}NAME-1,1):{0:if}NAME(({0:ap}NAME÷1)+({0:ap}NAME÷2),0,({0:agg}NAME)[({0:k}NAME-1,1))
.EQN 5 0 1724 0 0
({0:agg}NAME)[({0:k}NAME-1,2):{0:if}NAME(({0:ap}NAME÷1)+({0:ap}NAME÷2),-1,({0:agg}NAME)[({0:k}NAME-1,2))
.EQN 15 0 1408 0 0
{0:agg}NAME={150071}?_n_u_l_l_
.TXT 19 0 1301 0 0
Cg a72.000000,72.000000,146
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
denominator polynomial given by 1 + a}{\cf2\fs16\dn 1}{\cf2 z}{\cf2\fs16
\up -1}{\cf2  + a}{\cf2\fs16\dn 2}{\cf2 z}{\cf2\fs16\up -2}{\cf2  + a}{
\cf2\fs16\dn 3}{\cf2 z}{\cf2\fs16\up -3}{\cf2  + ..... for lowpass and 
highpass\par filters.  Ignore for bandpass and bandstop filters.}}
.EQN 7 0 1409 0 0
{0:NN}NAME:{0:if}NAME({0:REM}NAME÷1,{0:N}NAME+1,{0:N}NAME)
.EQN 5 0 1410 0 0
{0:n}NAME:0;{0:NN}NAME
.EQN 0 12 1411 0 0
{0:p}NAME:0;{0:NN}NAME
.EQN 0 16 1412 0 0
{0:NN}NAME={0}?_n_u_l_l_
.EQN 0 8 1413 0 0
{0:start}NAME={0}?_n_u_l_l_
.EQN 0 9 1414 0 0
{0:end}NAME={0}?_n_u_l_l_
.EQN 4 -45 1415 0 0
({0:af}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:af}NAME)[({0:m}NAME,{0:n}NAME))
.EQN 0 21 1416 0 0
{0:start}NAME:{0:if}NAME(({0:REM}NAME÷0)*({0:N}NAME>2),{0:start}NAME+1,{0:start}NAME)
.EQN 5 -21 1417 0 0
({0:afd}NAME)[(0,{0:n}NAME):({0:af}NAME)[(0,{0:n}NAME)
.EQN 0 13 1418 0 0
({0:afd}NAME)[(0,0):{0:if}NAME({0:N}NAME÷1,0,({0:aff}NAME)[(0,0))
.EQN 0 20 1419 0 0
({0:afd}NAME)[(0,0)={0}?_n_u_l_l_
.EQN 0 10 1420 0 0
({0:afd}NAME)[(0,1)={0}?_n_u_l_l_
.EQN 0 11 1421 0 0
({0:afd}NAME)[(0,2)={0}?_n_u_l_l_
.EQN 6 -54 1422 0 0
{0:m}NAME:{0:start}NAME;{0:end}NAME
.EQN 6 0 1423 0 0
({0:afd}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME(({0:N}NAME÷1)+({0:N}NAME÷2),({0:afd}NAME)[(0,{0:n}NAME),((0,{0:n}NAME,{0:p}NAME,({0:af}NAME)[({0:m}NAME,{0:p}NAME)*({0:afd}NAME)[({0:m}NAME-1,{0:n}NAME-{0:p}NAME)){64}))
.EQN 12 0 1424 0 0
{0:afd}NAME={0}?_n_u_l_l_
.EQN 11 0 1425 0 0
({0:afdd}NAME)[({0:n}NAME):({0:afd}NAME)[({0:end}NAME,{0:n}NAME)
.EQN 0 22 1894 0 0
{0:afddn}NAME:16000*{0:afdd}NAME
.EQN 26 -22 1905 0 0
{0:afdd}NAME={19007}?_n_u_l_l_
.EQN 0 26 1906 0 0
{0:afddn}NAME={0}?_n_u_l_l_
.EQN 13 -26 1903 0 0
({0:afdd}NAME){51}={18999}?_n_u_l_l_
.EQN 4 0 1904 0 0
({0:afddn}NAME){51}={18997}?_n_u_l_l_
.TXT 4 0 1431 0 0
Cg a72.000000,72.000000,144
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 The 
numerator polynomial given by 1 + a}{\cf2\fs16\dn 1}{\cf2 z}{\cf2\fs16
\up -1}{\cf2  + a}{\cf2\fs16\dn 2}{\cf2 z}{\cf2\fs16\up -2}{\cf2  + a}{
\cf2\fs16\dn 3}{\cf2 z}{\cf2\fs16\up -3}{\cf2  + ..... for lowpass and 
highpass\par filters.  Ignore for bandpass and bandstop filters.}}
.EQN 16 0 1438 0 0
({0:ag}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:ag}NAME)[({0:m}NAME,{0:n}NAME))
.EQN 5 0 1440 0 0
({0:agd}NAME)[(0,{0:n}NAME):({0:ag}NAME)[(0,{0:n}NAME)
.EQN 0 13 1441 0 0
({0:agd}NAME)[(0,0):{0:if}NAME({0:N}NAME÷1,0,({0:ag}NAME)[(0,0))
.EQN 0 20 1442 0 0
({0:agd}NAME)[(0,0)={0}?_n_u_l_l_
.EQN 0 10 1443 0 0
({0:agd}NAME)[(0,1)={0}?_n_u_l_l_
.EQN 0 11 1444 0 0
({0:agd}NAME)[(0,2)={0}?_n_u_l_l_
.EQN 12 -54 1446 0 0
({0:agd}NAME)[({0:m}NAME,{0:n}NAME):{0:if}NAME(({0:N}NAME÷1)+({0:N}NAME÷2),({0:agd}NAME)[(0,{0:n}NAME),((0,{0:n}NAME,{0:p}NAME,({0:ag}NAME)[({0:m}NAME,{0:p}NAME)*({0:agd}NAME)[({0:m}NAME-1,{0:n}NAME-{0:p}NAME)){64}))
.EQN 12 0 1447 0 0
{0:agd}NAME={0}?_n_u_l_l_
.EQN 8 0 1448 0 0
({0:agdd}NAME)[({0:n}NAME):({0:agd}NAME)[({0:end}NAME,{0:n}NAME)
.EQN 0 18 1889 0 0
{0:agdd}NAME:(1)/({0:maxb}NAME)*{0:agdd}NAME
.EQN 0 19 1896 0 0
{0:agddn}NAME:16000*{0:agdd}NAME
.EQN 41 -37 1449 0 0
{0:agdd}NAME={19007}?_n_u_l_l_
.EQN 0 32 1897 0 0
{0:agddn}NAME={0}?_n_u_l_l_
.EQN 18 -32 1891 0 0
({0:agdd}NAME){51}={18999}?_n_u_l_l_
.EQN 3 0 1900 0 0
({0:agddn}NAME){51}={18995}?_n_u_l_l_
.TXT 3 0 1450 0 0
Cg a72.000000,72.000000,99
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Denominator polynomial for bandpass and bandstop filters.  Ignore for 
lowpass and highpass filters.}}
.EQN 3 0 1451 0 0
{0:n}NAME:0;2*{0:N}NAME
.EQN 0 12 1452 0 0
{0:p}NAME:0;2*{0:N}NAME
.EQN 0 12 1453 0 0
{0:k1}NAME:0;{0:N}NAME-1
.EQN 4 -24 1454 0 0
({0:aff}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:aff}NAME)[({0:k1}NAME,{0:n}NAME))
.EQN 6 0 1455 0 0
({0:afd}NAME)[(0,{0:n}NAME):({0:aff}NAME)[(0,{0:n}NAME)
.EQN 6 0 1456 0 0
{0:k1}NAME:1;{0:N}NAME-1
.EQN 6 0 1457 0 0
({0:afd}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((0,{0:n}NAME,{0:p}NAME,({0:aff}NAME)[({0:k1}NAME,{0:p}NAME)*({0:afd}NAME)[({0:k1}NAME-1,{0:n}NAME-{0:p}NAME)){64}),0)
.EQN 19 -1 1458 0 0
{0:afd}NAME={150071}?_n_u_l_l_
.EQN 15 0 1459 0 0
({0:apsd}NAME)[({0:n}NAME):({0:afd}NAME)[({0:N}NAME-1,{0:n}NAME)
.EQN 22 2 1460 0 0
{0:apsd}NAME={150079}?_n_u_l_l_
.EQN 35 -1 1744 0 0
({0:apsd}NAME){51}={150074}?_n_u_l_l_
.TXT 4 0 1461 0 0
Cg a72.000000,72.000000,97
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue255;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2 
Numerator polynomial for bandpass and bandstop filters.  Ignore for 
lowpass and highpass filters.}}
.EQN 4 0 1462 0 0
{0:n}NAME:0;2*{0:N}NAME
.EQN 0 12 1463 0 0
{0:p}NAME:0;2*{0:N}NAME
.EQN 0 12 1464 0 0
{0:k1}NAME:0;{0:N}NAME-1
.EQN 4 -24 1465 0 0
({0:agg}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME({0:n}NAME>2,0,({0:agg}NAME)[({0:k1}NAME,{0:n}NAME))
.EQN 5 0 1466 0 0
({0:agd}NAME)[(0,{0:n}NAME):({0:agg}NAME)[(0,{0:n}NAME)
.EQN 6 0 1467 0 0
{0:k1}NAME:1;{0:N}NAME-1
.EQN 6 0 1468 0 0
({0:agd}NAME)[({0:k1}NAME,{0:n}NAME):{0:if}NAME(({0:type}NAME÷3)+({0:type}NAME÷4),((0,{0:n}NAME,{0:p}NAME,({0:agg}NAME)[({0:k1}NAME,{0:p}NAME)*({0:agd}NAME)[({0:k1}NAME-1,{0:n}NAME-{0:p}NAME)){64}),0)
.EQN 19 0 1469 0 0
{0:agd}NAME={150071}?_n_u_l_l_
.EQN 15 0 1470 0 0
({0:apsn}NAME)[({0:n}NAME):({0:agd}NAME)[({0:N}NAME-1,{0:n}NAME)
.EQN 23 2 1792 0 0
{0:apsn}NAME:(1)/({0:maxb}NAME)*{0:apsn}NAME
.EQN 26 -2 1471 0 0
{0:apsn}NAME={150079}?_n_u_l_l_
.EQN 20 0 1745 0 0
({0:apsn}NAME){51}={150071}?_n_u_l_l_