% m-file file name: tukhpf.m
% Function for designing FIR highpass filter using Tukey 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.
% a = parameter for Tukey window.  0 <= a <= 1.
% fchpf = cutoff frequency in Hz.
% fs = sampling rate in Hz.
% 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] = tukhpf(N,a,fchpf,fs)
Ts = 1/fs;  % Ts = sampling interval.
qchpf = 2*pi*fchpf*Ts; %qchpf = digital 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) = 1-(qchpf/pi);
      else hds(k) = -sin(qchpf*((k-1)-(N-1)/2))/(pi*((k-1)-(N-1)/2));
   end
end
for k = 1:N
   t(k)=k-1;
end
figure
stem(t,hds);grid;
title('Desired Shifted Response')
xlabel('Time')
ylabel('Amplitude')
disp('The desired shifted response is')
disp(hds)
%
% Calculating and plotting the window function.
%
for k = 1:N
   if k > (1+a)*(N-1)/2 + 1
      w(k) = (1/2)*[1 + cos((k-1-(1+a)*(N-1)/2)*pi*2/((1-a)*(N-1)))];
   elseif k >= (1-a)*(N-1)/2 + 1 & k <= (1+a)*(N-1)/2 + 1 w(k) = 1; 
   else
      w(k) = (1/2)*[1 + cos((N+1-k-1-(1+a)*(N-1)/2)*pi*2/((1-a)*(N-1)))];
   end   
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);
   H(n) = h((N-1)/2+1)+2*h(1)*cos(q(n)*(-(N-1)/2));
   for k = 2:(N-1)/2
      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);grid;
title('Magnitude Response')
xlabel('Frequency')
ylabel('Magnitude')
figure
plot(f,dB);grid;
title('Magnitude Response in dB')
xlabel('Frequency')
ylabel('Magnitude in dB')
figure
plot(f,pha);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)
grid on
hold on
plot(x,by) 
plot(real(dp),imag(dp),'rx')
plot(real(dz),imag(dz),'bo')
title('Digital Poles and Zeros')
xlabel('Real Part')
ylabel('Imaginary Part')
disp('Digital Pole Locations')
disp(dp)
disp('Digital Zero Locations')
disp(dz)