Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/signal-1.1.3/idct.m b/octave_packages/signal-1.1.3/idct.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 inverse 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 inverse discrete cosine transform x of X can be defined as follows:
+##
+##          N-1
+##   x[n] = sum w(k) X[k] cos (pi (2n+1) k / 2N ),  n = 0, ..., N-1
+##          k=0
+##
+## with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1
+##
+## See also: idct, dct2, idct2, dctmtx
+
+function y = idct (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 (n-nr+1 : n, :) = [];
+  endif
+
+  if ( realx && rem (n, 2) == 0 )
+    w = [ sqrt(n/4); sqrt(n/2)*exp((1i*pi/2/n)*[1:n-1]') ] * ones (1, nc);
+    y = ifft (w .* x);
+    y([1:2:n, n:-2:1], :) = 2*real(y);
+  elseif n == 1
+    y = x;
+  else
+    ## reverse the steps of dct using inverse operations
+    ## 1. undo post-fft scaling
+    w = [ sqrt(4*n); sqrt(2*n)*exp((1i*pi/2/n)*[1:n-1]') ] * ones (1, nc);
+    y = x.*w;
+
+    ## 2. reconstruct fft result and invert it
+    w = exp(-1i*pi*[n-1:-1:1]'/n) * ones(1,nc);
+    y = ifft ( [ y ; zeros(1,nc); y(n:-1:2,:).*w ] );
+
+    ## 3. keep only the original data; toss the reversed copy
+    y = y(1:n, :);
+    if (realx) y = real (y); endif
+  endif
+  if transpose, y = y.'; endif
+
+endfunction