.MCAD 303010000 1 74 128 0
.CMD PLOTFORMAT
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15 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
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=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
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.TXT 8 1 108 0
Cg a68.875000,73.000000,524
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Mathcad file name: equal.mcd\par 
\par This Mathcad program simulates transversal
 equalizer.  The input is generated by a
 linear\par feedback shift register.  A 
pseudorandom sequence is generated.  The
 system is simulated\par by an RC filter.
  The time constant }{\f1 t}{ = RC can be
 adjusted.  The output of the system is\par 
obtained by convolving the input x}{\fs16 
\dn6 j}{ with the impulse response h}{\fs16 
\dn6 j}{.  The pulse duration is 1s and\par 
the number of samples per bit is NoS.\par 
\par Generating input sequence a0}{\fs16 
\dn6 j}{.}}
}
.EQN 21 0 7 0
({0:a0}NAME)[(0):1
.EQN 0 8 8 0
({0:a1}NAME)[(0):1
.EQN 0 8 9 0
({0:a2}NAME)[(0):1
.EQN 0 8 10 0
({0:a3}NAME)[(0):1
.EQN 0 8 11 0
({0:a4}NAME)[(0):1
.EQN 0 8 12 0
({0:a5}NAME)[(0):1
.EQN 0 8 13 0
({0:a6}NAME)[(0):1
.EQN 0 7 21 0
{0:NoB}NAME:7
.EQN 5 -55 6 0
{0:n}NAME:1;(2)^({0:NoB}NAME)-1
.TXT 0 17 109 0
Cg a34.875000,56.000000,51
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {NoB is the number of bits of the
 input sequence.}}
}
.EQN 15 -17 5 0
({7,1}ö({0:a6}NAME)[({0:n}NAME)ö({0:a5}NAME)[({0:n}NAME)ö({0:a4}NAME)[({0:n}NAME)ö({0:a3}NAME)[({0:n}NAME)ö({0:a2}NAME)[({0:n}NAME)ö({0:a1}NAME)[({0:n}NAME)ö({0:a0}NAME)[({0:n}NAME)):({7,1}ö{0:mod}NAME(({0:a0}NAME)[({0:n}NAME-1)+({0:a1}NAME)[({0:n}NAME-1)
,2)ö({0:a6}NAME)[({0:n}NAME-1)ö({0:a5}NAME)[({0:n}NAME-1)ö({0:a4}NAME)[({0:n}NAME-1)ö({0:a3}NAME)[({0:n}NAME-1)ö({0:a2}NAME)[({0:n}NAME-1)ö({0:a1}NAME)[({0:n}NAME-1))
.EQN 16 1 16 0
{0:NoS}NAME:16
.TXT 0 13 17 0
Cg a27.375000,59.000000,40
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {NoS is the number of samples per
 bit.}}
}
.EQN 4 -13 18 0
{0:k}NAME:0;{0:NoS}NAME-1
.EQN 0 14 26 0
{0:n}NAME:0;(2)^({0:NoB}NAME)-1
.EQN 4 -14 19 0
({0:x}NAME)[({0:NoS}NAME*{0:n}NAME+{0:k}NAME):{0:if}NAME(({0:a0}NAME)[({0:n}NAME)÷0,-1,{0}1)
.TXT 0 24 110 0
Cg a27.125000,48.000000,56
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {x}{\fs16 \dn6 j}{ are the samples
 of the input signal.}}
}
.EQN 5 -24 20 0
{0:j}NAME:0;((2)^({0:NoB}NAME)-1)*{0:NoS}NAME
.EQN 0 21 33 0
{0:m}NAME:0;((2)^({0:NoB}NAME)-1)*{0:NoS}NAME
.EQN 26 -22 27 0
2&-2&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:j}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:j}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 58 15 0 3 
.EQN 25 0 32 0
{0:\t}NAME:2
.EQN 0 24 37 0
{0:N}NAME:{0:floor}NAME(11*{0:NoS}NAME*{0:\t}NAME)
.TXT 5 -2 126 0
Cg a31.125000,32.000000,79
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {11 times the (time constant) * 
(NoS) is the length of the impulse response.}}
}
.EQN 2 -22 36 0
({0:h}NAME)[({0:j}NAME):{0:if}NAME({0:j}NAME<{0:N}NAME,({0:e}NAME)^(-(({0:j}NAME)/({0:NoS}NAME*{0:\t}NAME))),0)
.EQN 8 1 38 0
({0:y}NAME)[({0:m}NAME):{0:if}NAME({0:m}NAME<{0:N}NAME,((0,{0:m}NAME,{0:j}NAME,({0:x}NAME)[({0:j}NAME)*({0:h}NAME)[({0:m}NAME-{0:j}NAME)){64}),(({0:m}NAME-{0:N}NAME+1,{0:m}NAME,{0:j}NAME,({0:x}NAME)[({0:j}NAME)*({0:h}NAME)[({0:m}NAME-{0:j}NAME)){64}))
.EQN 0 41 40 0
({0:y}NAME)[({0:m}NAME):(1)/({0:NoS}NAME)*({0:y}NAME)[({0:m}NAME)
.TXT 0 13 127 0
Cg a14.250000,18.000000,46
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {y}{\fs16 \dn6 m}{ are the RC filter
 output.}}
}
.EQN 6 -55 39 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:y}NAME)[({0:m}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:m}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 57 18 0 3 
.EQN 30 0 42 0
{0:n}NAME:0;(2)^({0:NoB}NAME)-2
.EQN 5 0 41 0
({0:ys}NAME)[({0:n}NAME):({0:y}NAME)[({0:NoS}NAME*({0:n}NAME+1))
.TXT 0 18 128 0
Cg a47.000000,55.000000,112
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {ys}{\fs16 \dn6 n}{ are samples 
of the filter output.  These samples are
 applied\par to the transversal equalizer.}}
}
.EQN 19 -18 43 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:ys}NAME)[({0:n}NAME),0@&&(_n_u_l_l_&_n_u_l_l_)&{0:n}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 0 0 2 NO-TRACE-STRING
0 0 1 2 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 59 15 0 3 
.EQN 25 1 45 0
{0:n1}NAME:0;10
.EQN 4 0 46 0
({0:pr}NAME)[({0:n1}NAME):({0:h}NAME)[(({0:n1}NAME+1)*{0:NoS}NAME)
.TXT 0 19 111 0
Cg a43.125000,53.000000,65
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {pr are samples of the RC filter
 output to a rectangular pulse.}}
}
.EQN 10 -17 73 0
({3,1}ö{0:ca1}NAMEö{0:ca0}NAMEö{0:cam1}NAME):(({3,3}ö({0:pr}NAME)[(0)ö0ö0ö({0:pr}NAME)[(1)ö({0:pr}NAME)[(0)ö0ö({0:pr}NAME)[(2)ö({0:pr}NAME)[(1)ö({0:pr}NAME)[(0)))^(-1)*({3,1}ö0ö1ö0)
.EQN 9 -3 74 0
{0:cam1}NAME={0}?_n_u_l_l_
.EQN 0 12 75 0
{0:ca0}NAME={0}?_n_u_l_l_
.EQN 0 13 76 0
{0:ca1}NAME={0}?_n_u_l_l_
.EQN 4 -25 80 0
{0:n}NAME:2;(2)^({0:NoB}NAME)-2
.EQN 0 14 81 0
({0:yo}NAME)[(1):({0:ys}NAME)[(0)
.EQN 4 -14 78 0
({0:yo}NAME)[({0:n}NAME):{0:cam1}NAME*({0:ys}NAME)[({0:n}NAME)+{0:ca0}NAME*({0:ys}NAME)[({0:n}NAME-1)+{0:ca1}NAME*({0:ys}NAME)[({0:n}NAME-2)
.TXT 0 34 113 0
Cg a33.500000,39.000000,64
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {yo}{\fs16 \dn6 n}{ are samples 
at the output of the equalizer.}}
}
.EQN 5 -34 86 0
{0:n}NAME:1;(2)^({0:NoB}NAME)-2
.EQN 39 1 82 0
({0:a0}NAME)[({0:j}NAME)=
.EQN 0 3 83 0
({0:yo}NAME)[({0:n}NAME)=
.TXT 1 21 114 0
Cg a42.500000,48.000000,108
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {a0 are input data, yo are samples
 of the equalizer output,\par ys are samples
 at the input of the equalizer.}}
}
.EQN 1 -15 87 0
({0:ys}NAME)[({0:n}NAME)=
.EQN 120 -10 89 0
{0:n}NAME:0;(2)^({0:NoB}NAME)-2
.EQN 4 0 96 0
({0:ap}NAME)[({0:n}NAME+1):{0:if}NAME(({0:a0}NAME)[({0:n}NAME)÷0,-1,1)
.EQN 4 0 95 0
{0:n}NAME:1;(2)^({0:NoB}NAME)-2
.EQN 0 14 101 0
({0:ap}NAME)[(1)={0}?_n_u_l_l_
.EQN 0 9 103 0
({0:yo}NAME)[(1)={0}?_n_u_l_l_
.EQN 6 -23 88 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:ap}NAME)[({0:n}NAME)-({0:yo}NAME)[({0:n}NAME),0@&&(_n_u_l_l_&_n_u_l_l_)&{0:n}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 0 0 2 NO-TRACE-STRING
0 0 1 2 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 60 15 0 3 
.EQN 24 1 104 0
{0:n}NAME:1;(2)^({0:NoB}NAME)-2
.EQN 2 -1 105 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:ap}NAME)[({0:n}NAME+1)-({0:ys}NAME)[({0:n}NAME),0@&&(_n_u_l_l_&_n_u_l_l_)&{0:n}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 0 0 2 NO-TRACE-STRING
0 0 1 2 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 58 15 0 3 
.TXT 37 1 115 0
Cg a62.875000,72.000000,187
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Calculating the probability of 
error with and without transversal equalizer.
  Pew is the \par probability of error with
 equalizer, and Pewo is the probability 
of error without equalizer. }}
}
.EQN 9 0 118 0
{0:NoEW}NAME:((1,(2)^({0:NoB}NAME)-2,{0:n}NAME,{0:if}NAME((({0:ap}NAME)[({0:n}NAME)÷1)*(({0:yo}NAME)[({0:n}NAME)<0)+(({0:ap}NAME)[({0:n}NAME)÷-1)*(({0:yo}NAME)[({0:n}NAME)>0),1,0)){64})
.EQN 0 52 119 0
{0:NoEW}NAME={0}?_n_u_l_l_
.EQN 8 -53 120 0
{0:Pew}NAME:({0:NoEW}NAME)/((2)^({0:NoB}NAME)-2)
.EQN 0 17 121 0
{0:Pew}NAME={0}?_n_u_l_l_
.EQN 9 -16 122 0
{0:NoEWO}NAME:((1,(2)^({0:NoB}NAME)-2,{0:n}NAME,{0:if}NAME((({0:ap}NAME)[({0:n}NAME)÷1)*(({0:ys}NAME)[({0:n}NAME)<0)+(({0:ap}NAME)[({0:n}NAME)÷-1)*(({0:ys}NAME)[({0:n}NAME)>0),1,0)){64})
.EQN 0 52 123 0
{0:NoEWO}NAME={0}?_n_u_l_l_
.EQN 8 -53 124 0
{0:Pewo}NAME:({0:NoEWO}NAME)/((2)^({0:NoB}NAME)-2)
.EQN 0 17 125 0
{0:Pewo}NAME={0}?_n_u_l_l_