## 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, see <http://www.gnu.org/licenses/>. ## T = dctmtx (n) ## Return the DCT transformation matrix of size n x n. ## ## If A is an n x n matrix, then the following are true: ## T*A == dct(A), T'*A == idct(A) ## T*A*T' == dct2(A), T'*A*T == idct2(A) ## ## A dct transformation matrix is useful for doing things like jpeg ## image compression, in which an 8x8 dct matrix is applied to ## non-overlapping blocks throughout an image and only a subblock on the ## top left of each block is kept. During restoration, the remainder of ## the block is filled with zeros and the inverse transform is applied ## to the block. ## ## See also: dct, idct, dct2, idct2 ## Author: Paul Kienzle <pkienzle@users.sf.net> ## 2001-02-08 ## * initial release function T = dctmtx(n) if nargin != 1 usage("T = dctmtx(n)") endif if n > 1 T = [ sqrt(1/n)*ones(1,n) ; \ sqrt(2/n)*cos((pi/2/n)*([1:n-1]'*[1:2:2*n])) ]; elseif n == 1 T = 1; else error ("dctmtx: n must be at least 1"); endif endfunction

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