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view main/signal/czt.m @ 0:6b33357c7561 octave-forge
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author | pkienzle |
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date | Wed, 10 Oct 2001 19:54:49 +0000 |
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children | 6cd6668c225b |
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## Copyright (C) 2000 Paul Kienzle ## ## 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 2 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, write to the Free Software ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA ## 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(-2i*pi*(f2-f1)/(m*Fs)); ## freq. step of f2-f1/m ## a = exp(2i*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(2i*pi/m), a=1 ## Because it is computed with three FFTs, this will be faster than ## computing the fourier transform directly for large m (which is ## otherwise the best you can do with fft(x,n) for n prime). ## TODO: More testing---particularly when m+N-1 approaches a power of 2 ## TODO: Consider treating w,a as f1,f2 expressed in radians if w is real function y = czt(x, m, w, a) if nargin < 1 || nargin > 4, usage("y=czt(x, m, w, a)"); endif if nargin < 2 || isempty(m), m = length(x); endif if nargin < 3 || isempty(w), w = exp(2i*pi/m); endif if nargin < 4 || isempty(a), a = 1; endif N = length(x); if (columns(x) == 1) k = [0:m-1]'; Nk = [-(N-1):m-2]'; else k = [0:m-1]; Nk = [-(N-1):m-2]; endif nfft = 2^nextpow2(min(m,N)+length(Nk)-1); Wk2 = w.^(-(Nk.^2)/2); AWk2 = (a.^-k) .* (w.^((k.^2)/2)); y = ifft(fft(postpad(Wk2,nfft)).*fft(postpad(x,nfft).*postpad(AWk2,nfft))); y = w.^((k.^2)/2).*y(1+N:m+N); endfunction