Created
March 11, 2023 11:19
-
-
Save mattdsp/dde270c64ace9d7bcad30333c6b9c90a to your computer and use it in GitHub Desktop.
Frequency sampling design of linear phase FIR filters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
function h = fsamp(mag,N) | |
% function h = fsamp(mag,N) | |
% frequency sampling design of linear phase FIR filter | |
% | |
% mag ... desired magnitude response on an equidistant grid | |
% between 0 and Nyquist | |
% N ... filter length (N <= 2*length(mag) - 1 ) | |
% | |
% for even N the frequency grid is defined by (M = length(mag)): | |
% | |
% f_k = k/(M-1), k=0,1,...,M-1 (includes Nyquist = 1) | |
% | |
% for odd N the grid is f_k = 2/(2*M-1), k=0,1,...,M-1 (Nyquist is not included!) | |
% | |
% M. Lang, mattsdspblog@gmail.com | |
M = length(mag); | |
Neven = (rem(N,2) == 0); | |
if Neven, | |
n = 2*(M-1); % FFT length | |
if ( N > n ), | |
error('fsamp: filter length N must not be greater than 2*(length(mag)-1).'); | |
end | |
w = (0:M-1)'/(M-1)*pi; % frequency grid | |
D = mag(:).*exp(-1i*w*(n-1)/2); % desired complex frequency response | |
D = [D;conj(D(M-1:-1:2))]; % extend to 2*Nyquist | |
else | |
n = 2*M-1; | |
if ( N > n ), | |
error('fsamp: filter length N must not be greater than 2*(length(mag)-1).'); | |
end | |
w = (0:M-1)'*2*pi/(2*M-1); | |
D = mag(:).*exp(-1i*w*(n-1)/2); | |
D = [D;conj(D(M:-1:2))]; | |
end | |
% impulse response via IFFT | |
h = real(ifft(D)); | |
% windowing (Hamming) | |
I = (n-N)/2+1; | |
ww = hamming(N); | |
h = h(I:I+N-1).*ww(:); | |
return |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment