/usr/share/octave/packages/signal-1.3.0/idct.m is in octave-signal 1.3.0-1.
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 | ## 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} {@var{y} =} idct (@var{x})
## @deftypefnx {Function File} {@var{y} =} idct (@var{x}, @var{n})
## Compute the inverse 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 even length.
##
## The inverse discrete cosine transform @var{x} can be defined as follows:
##
## @example
## N-1
## x[n] = sum w(k) X[k] cos (pi (2n+1) k / 2N ), n = 0, ..., N-1
## k=0
## @end example
##
## with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1
##
## @seealso{dct, dct2, idct2, dctmtx}
## @end deftypefn
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
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