/usr/share/octave/packages/signal-1.3.2/dct.m is in octave-signal 1.3.2-1+b1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | ## 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/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} dct (@var{x})
## @deftypefnx {Function File} {} dct (@var{x}, @var{n})
## Compute the discrete cosine transform of @var{x}. If @var{n} is given,
## then @var{x} is padded or trimmed to length @var{n} before computing the
## transform. If @var{x} is a matrix, compute the transform along the columns
## of the the matrix. The transform is faster if @var{x} is real-valued and
## has even length.
##
## The discrete cosine transform @var{x} can be defined as follows:
##
## @example
## @group
## N-1
## X[k] = w(k) sum x[n] cos (pi (2n+1) k / 2N ), k = 0, ..., N-1
## n=0
## @end group
## @end example
##
## 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.
##
## @seealso{idct, dct2, idct2, dctmtx}
## @end deftypefn
## 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
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