Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / czt.m

diff --git a/octave_packages/signal-1.1.3/czt.m b/octave_packages/signal-1.1.3/czt.m
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+## 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 <http://www.gnu.org/licenses/>.
+
+## 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);