Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/signal-1.1.3/rceps.m b/octave_packages/signal-1.1.3/rceps.m
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+## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
+##
+## 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, xm] = rceps(x)
+##   Produce the cepstrum of the signal x, and if desired, the minimum
+##   phase reconstruction of the signal x.  If x is a matrix, do so
+##   for each column of the matrix.
+##
+## Example
+##   f0=70; Fs=10000;           # 100 Hz fundamental, 10kHz sampling rate
+##   a=poly(0.985*exp(1i*pi*[0.1, -0.1, 0.3, -0.3])); # two formants
+##   s=0.005*randn(1024,1);      # Noise excitation signal
+##   s(1:Fs/f0:length(s)) = 1;   # Impulse glottal wave
+##   x=filter(1,a,s);            # Speech signal in x
+##   [y, xm] = rceps(x.*hanning(1024)); # cepstrum and min phase reconstruction
+##
+## Reference
+##    Programs for digital signal processing. IEEE Press.
+##    New York: John Wiley & Sons. 1979.
+
+function [y, ym] = rceps(x)
+  if (nargin != 1)
+    print_usage;
+  end
+  y = real(ifft(log(abs(fft(x)))));
+  if nargout == 2
+    n=length(x);
+    if rows(x)==1
+      if rem(n,2)==1
+        ym = [y(1), 2*y(2:n/2), zeros(1,n/2-1)];
+      else
+        ym = [y(1), 2*y(2:n/2), y(n/2+1), zeros(1,n/2-1)];
+      endif
+    else
+      if rem(n,2)==1
+        ym = [y(1,:); 2*y(2:n/2,:); zeros(n/2-1,columns(y))];
+      else
+        ym = [y(1,:); 2*y(2:n/2,:); y(n/2+1,:); zeros(n/2-1,columns(y))];
+      endif
+    endif
+    ym = real(ifft(exp(fft(ym))));
+  endif
+endfunction
+
+%!error rceps
+%!error rceps(1,2)  # too many arguments
+
+%!test
+%! ## accepts matrices
+%! x=randn(32,3);
+%! [y, xm] = rceps(x);
+%! ## check the mag-phase response of the reproduction
+%! hx = fft(x);
+%! hxm = fft(xm);
+%! assert(abs(hx), abs(hxm), 200*eps); # good magnitude response match
+%! #XXX FIXME XXX test for minimum phase?  Stop using random datasets!
+%! #assert(arg(hx) != arg(hxm));        # phase mismatch
+
+%!test
+%! ## accepts column and row vectors
+%! x=randn(256,1);
+%! [y, xm] = rceps(x);
+%! [yt, xmt] = rceps(x.');
+%! tol = 1e-14;
+%! assert(yt.', y, tol);
+%! assert(xmt.', xm, tol);
+
+%!demo
+%! f0=70; Fs=10000;           # 100 Hz fundamental, 10kHz sampling rate
+%! a=real(poly(0.985*exp(1i*pi*[0.1, -0.1, 0.3, -0.3]))); # two formants
+%! s=0.05*randn(1024,1);      # Noise excitation signal
+%! s(floor(1:Fs/f0:length(s))) = 1;  # Impulse glottal wave
+%! x=filter(1,a,s);           # Speech signal in x
+%! [y, xm] = rceps(x);        # cepstrum and minimum phase x
+%! [hx, w] = freqz(x,1,[],Fs); hxm = freqz(xm);
+%! figure(1);
+%! subplot(311);
+%!    auplot(x,Fs,'b',';signal;');
+%!    hold on; auplot(xm,Fs,'g',';reconstruction;');
+%!    hold off;
+%! subplot(312);
+%!    axis("ticy");
+%!    plot(w,log(abs(hx)), ";magnitude;", ...
+%!         w,log(abs(hxm)),";reconstruction;");
+%! subplot(313);
+%!    axis("on");
+%!    plot(w,unwrap(arg(hx))/(2*pi), ";phase;",...
+%!        w,unwrap(arg(hxm))/(2*pi),";reconstruction;");
+%! figure(2); auplot(y,Fs,';cepstrum;');
+%! %-------------------------------------------------------------
+%! % confirm the magnitude spectrum is identical in the signal
+%! % and the reconstruction and that there are peaks in the
+%! % cepstrum at 14 ms intervals corresponding to an F0 of 70 Hz.