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view main/signal/idct.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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## Copyright (C) 2001 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 ## 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 ), k = 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 ## Author: Paul Kienzle ## 2001-02-08 ## * initial release function y = idct (x, n) if (nargin < 1 || nargin > 2) usage ("y = dct(x [, n])"); 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