% m-file file name: dolbpf.m
% FUnction for designing FIR bandpass filter using Dolph-Chebyshev window.
% Written by Dr. James S. Kang, Professor
% Department of Electrical and Computer Engineering
% California State Polytechnic University, Pomona
% N = length (order) of the filter (impulse response).
% r = ripple ratio for Dolph-Chebyshev window. 0 < r < 1.
% f1bsf = lower passband cutoff frequency.
% f2bsf = upper passband cutoff frequency. f1bsf<f2bsf<fs/2.
% fs = sampling rate in Hz.
% To run the program, try >>dolbpf(21,0.1,2000,3000,10000) <Enter> or
% >>dolbpf(21,0.1,0.2,0.3,1) <Enter>.
% References:
% Leland B. Jackson, Digital Filters and Signal Processing, 3rd ed., Kluwer Academic Publishers, 1996.
% T. W. Parks and C. S. Burrus, Digital Filter Design, John Wiley and Sons, Inc., 1987.
% Andreas Antoniou, Digital Filters: Analysis, Design, and Applications, 2nd ed., McGraw-Hill, 1993.
% J. G. Proakis and D. G. Manolakis, Digital Signal Processing, 3rd ed., Prentice-Hall, 1996.
% A. V. Oppenheim and R. W. Shafer, Discrete-Time Signal Processing, Prentice-Hall, 1989.
function[h,H] = dolbpf(N,r,f1bpf,f2bpf,fs)
Ts = 1/fs;  % Ts = sampling interval.
q1bpf = 2*pi*f1bpf*Ts; % q1bpf = digital lower passband cutoff frequency.
q2bpf = 2*pi*f2bpf*Ts; % q2bpf = digital upper passband cutoff frequency.
%
% Calculating the desired shifted response.
%
%if rem(N,2) == 0 N = N+1; end;
disp('The length (order) of the filter is')
disp(N)
for k = 1:N
  if (k-1) ~= (N-1)/2
   hds(k) = sin(q2bpf*(k-1-(N-1)/2))/(pi*(k-1-(N-1)/2))-sin(q1bpf*(k-1-(N-1)/2))/(pi*(k-1-(N-1)/2));
  else
   hds(k) = q2bpf/pi - q1bpf/pi;
  end
end
disp('The desired shifted response is')
disp(hds)
%
% Calculating and plotting the window function.
%
if N > 1 x0 = cosh((1/(N-1))*acosh(1/r)); else x0 = 0; end
for k = 1:N
   w(k) = (1/N)*(1/r);
   for i = 1:(N-1)/2
      x = x0*cos(i*pi/N);
      if x >= -1 & x <= 1 T = cos((N-1)*acos(x)); 
      else T = cosh(acosh(x));
      end
      w(k) = w(k) + (1/N)*2*T*cos(2*(k-1-(N-1)/2)*pi*i/N);
   end
end
scale=1/w((N-1)/2);
for k = 1:N
   w(k) = scale*w(k);
end
for k = 1:N
   t(k) = k-1; 
   z(k) = 0; 
   if w(k) >= 0 Hi(k) = w(k); Lo(k) = 0; 
      else Hi(k) = 0; Lo(k) = -w(k); 
   end
end
figure
stem(t,w);grid;
%errorbar(t,z,Lo,Hi,'w')
title('Window Function')
xlabel('Time')
ylabel('Amplitude')
disp('The window function is')
disp(w)
%
% Calculating and plotting the impulse response of the FIR filter.
%
for k = 1:N
   h(k) = hds(k)*w(k);
end
for k = 1:N
   t(k) = k-1; 
   z(k) = 0; 
   if h(k) >= 0 Hi(k) = h(k); Lo(k) = 0; 
      else Hi(k) = 0; Lo(k) = -h(k); 
   end
end
figure
stem(t,h);grid;
%errorbar(t,z,Lo,Hi,'h')
title('Impulse Response')
xlabel('Time')
ylabel('Amplitude')
disp('The impulse response is')
disp(h)
%
% Calculating and plotting the frequency response.
%
M = 400;
for n = 1:M+1
   f(n) = (n-1)/M;
   q(n) = 2*pi*f(n);
   if rem(N,2) == 1
        H(n) = h((N-1)/2+1)+2*h(1)*cos(q(n)*(-(N-1)/2));
   else
        H(n) = 2*h(1)*cos(q(n)*(-(N-1)/2));
   end
   if rem(N,2) == 1 endk = (N-1)/2; else endk = N/2; end
   for k = 2:endk
      H(n) = H(n) + 2*h(k)*cos(q(n)*(k-1-(N-1)/2));
   end
   H(n) = exp(-j*q(n)*(N-1)/2)*H(n);
   mag(n) = abs(H(n));
   dB(n) = 20*log10(abs(H(n)));
   if dB(n) < -200 dB(n) = -200; end
   pha(n) = angle(H(n))/pi; 
end
figure
plot(f,mag,'y-');grid;
title('Magnitude Response')
xlabel('Frequency')
ylabel('Magnitude')
figure
plot(f,dB,'y-');grid;
title('Magnitude Response in dB')
xlabel('Frequency')
ylabel('Magnitude in dB')
figure
plot(f,pha,'y-');grid;
title('Phase Response')
xlabel('Frequency')
ylabel('Phase in Radians')
%
% Calculating and plotting poles and zeros.
%
nozeros = 0;
k = 1;
while abs(h(k)) < 10^(-10) & k == nozeros + 1 & k < (N-1)/2
   nozeros = nozeros + 1;
   k = k+1;
end
stop = N - 2*nozeros;
for k = 1:stop
  h1(k) = h(k+nozeros);
end
dz=ROOTS(h1);
for k = 1:stop-1
  dp(k) = 0;
end
for m = 1:201
   x(m) = (m-101)/100;
   ty(m) = sqrt(1-x(m).*x(m));
   by(m) = - ty(m);
end
figure
plot(x,ty,'w-')
grid on
hold on
plot(x,by,'w-') 
plot(real(dp),imag(dp),'rx')
plot(real(dz),imag(dz),'yo')
title('Digital Poles and Zeros')
xlabel('Real Part')
ylabel('Imaginary Part')
disp('Digital Pole Locations')
disp(dp)
disp('Digital Zero Locations')
disp(dz)