## [r11630]: trunk / octave-forge / main / signal / inst / czt.m Maximize Restore History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83``` ```## Copyright (C) 2004 Daniel Gunyan ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## usage y=czt(x, m, w, a) ## ## Chirp z-transform. Compute the frequency response starting at a and ## stepping by w for m steps. a is a point in the complex plane, and ## w is the ratio between points in each step (i.e., radius increases ## exponentially, and angle increases linearly). ## ## To evaluate the frequency response for the range f1 to f2 in a signal ## with sampling frequency Fs, use the following: ## m = 32; ## number of points desired ## w = exp(-j*2*pi*(f2-f1)/((m-1)*Fs)); ## freq. step of f2-f1/m ## a = exp(j*2*pi*f1/Fs); ## starting at frequency f1 ## y = czt(x, m, w, a); ## ## If you don't specify them, then the parameters default to a fourier ## transform: ## m=length(x), w=exp(-j*2*pi/m), a=1 ## ## If x is a matrix, the transform will be performed column-by-column. ## Algorithm (based on Oppenheim and Schafer, "Discrete-Time Signal ## Processing", pp. 623-628): ## make chirp of length -N+1 to max(N-1,M-1) ## chirp => w^([-N+1:max(N-1,M-1)]^2/2) ## multiply x by chirped a and by N-elements of chirp, and call it g ## convolve g with inverse chirp, and call it gg ## pad ffts so that multiplication works ## ifft(fft(g)*fft(1/chirp)) ## multiply gg by M-elements of chirp and call it done function y = czt(x, m, w, a) if nargin < 1 || nargin > 4, print_usage; endif [row, col] = size(x); if row == 1, x = x(:); col = 1; endif if nargin < 2 || isempty(m), m = length(x(:,1)); endif if length(m) > 1, error("czt: m must be a single element\n"); endif if nargin < 3 || isempty(w), w = exp(-2*j*pi/m); endif if nargin < 4 || isempty(a), a = 1; endif if length(w) > 1, error("czt: w must be a single element\n"); endif if length(a) > 1, error("czt: a must be a single element\n"); endif ## indexing to make the statements a little more compact n = length(x(:,1)); N = [0:n-1]'+n; NM = [-(n-1):(m-1)]'+n; M = [0:m-1]'+n; nfft = 2^nextpow2(n+m-1); # fft pad W2 = w.^(([-(n-1):max(m-1,n-1)]'.^2)/2); # chirp for idx = 1:col fg = fft(x(:,idx).*(a.^-(N-n)).*W2(N), nfft); fw = fft(1./W2(NM), nfft); gg = ifft(fg.*fw, nfft); y(:,idx) = gg(M).*W2(M); endfor if row == 1, y = y.'; endif endfunction %!shared x %! x = [1,2,4,1,2,3,5,2,3,5,6,7,8,4,3,6,3,2,5,1]; %!assert(fft(x),czt(x),10000*eps); %!assert(fft(x'),czt(x'),10000*eps); %!assert(fft([x',x']),czt([x',x']),10000*eps); ```