Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/signal-1.1.3/dct.m b/octave_packages/signal-1.1.3/dct.m
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+## Copyright (C) 2001 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/>.
+
+## y = dct (x, n)
+##    Computes the discrete cosine transform of x.  If n is given, then
+##    x is padded or trimmed to length n before computing the transform.
+##    If x is a matrix, compute the transform along the columns of the
+##    the matrix. The transform is faster if x is real-valued and even
+##    length.
+##
+## The discrete cosine transform X of x can be defined as follows:
+##
+##               N-1
+##   X[k] = w(k) sum x[n] cos (pi (2n+1) k / 2N ),  k = 0, ..., N-1
+##               n=0
+##
+## with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1.  There
+## are other definitions with different scaling of X[k], but this form
+## is common in image processing.
+##
+## See also: idct, dct2, idct2, dctmtx
+
+## From Discrete Cosine Transform notes by Brian Evans at UT Austin,
+## http://www.ece.utexas.edu/~bevans/courses/ee381k/lectures/09_DCT/lecture9/
+## the discrete cosine transform of x at k is as follows:
+##
+##          N-1
+##   X[k] = sum 2 x[n] cos (pi (2n+1) k / 2N )
+##          n=0
+##
+## which can be computed using:
+##
+##   y = [ x ; flipud (x) ]
+##   Y = fft(y)
+##   X = exp( -j pi [0:N-1] / 2N ) .* Y
+##
+## or for real, even length x
+##
+##   y = [ even(x) ; flipud(odd(x)) ]
+##   Y = fft(y)
+##   X = 2 real { exp( -j pi [0:N-1] / 2N ) .* Y }
+##
+## Scaling the result by w(k)/2 will give us the desired output.
+
+function y = dct (x, n)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage;
+  endif
+
+  realx = isreal(x);
+  transpose = (rows (x) == 1);
+
+  if transpose, x = x (:); endif
+  [nr, nc] = size (x);
+  if nargin == 1
+    n = nr;
+  elseif n > nr
+    x = [ x ; zeros(n-nr,nc) ];
+  elseif n < nr
+    x (nr-n+1 : n, :) = [];
+  endif
+
+  if n == 1
+    w = 1/2;
+  else
+    w = [ sqrt(1/4/n); sqrt(1/2/n)*exp((-1i*pi/2/n)*[1:n-1]') ] * ones (1, nc);
+  endif
+  if ( realx && rem (n, 2) == 0 )
+    y = fft ([ x(1:2:n,:) ; x(n:-2:1,:) ]);
+    y = 2 * real( w .* y );
+  else
+    y = fft ([ x ; flipud(x) ]);
+    y = w .* y (1:n, :);
+    if (realx) y = real (y); endif
+  endif
+  if transpose, y = y.'; endif
+
+endfunction