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Initial revision
author pkienzle
date Wed, 10 Oct 2001 19:54:49 +0000
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-1:000000000000 0:6b33357c7561
1 ## Copyright (C) 2001 Paul Kienzle
2 ##
3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 2 of the License, or
6 ## (at your option) any later version.
7 ##
8 ## This program is distributed in the hope that it will be useful,
9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 ## GNU General Public License for more details.
12 ##
13 ## You should have received a copy of the GNU General Public License
14 ## along with this program; if not, write to the Free Software
15 ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
16
17 ## y = dct (x, n)
18 ## Computes the inverse discrete cosine transform of x. If n is
19 ## given, then x is padded or trimmed to length n before computing
20 ## the transform. If x is a matrix, compute the transform along the
21 ## columns of the the matrix. The transform is faster if x is
22 ## real-valued and even length.
23 ##
24 ## The inverse discrete cosine transform x of X can be defined as follows:
25 ##
26 ## N-1
27 ## x[n] = sum w(k) X[k] cos (pi (2n-1) k / 2N ), k = 0, ..., N-1
28 ## k=0
29 ##
30 ## with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1
31 ##
32 ## See also: idct, dct2, idct2, dctmtx
33
34 ## Author: Paul Kienzle
35 ## 2001-02-08
36 ## * initial release
37 function y = idct (x, n)
38
39 if (nargin < 1 || nargin > 2)
40 usage ("y = dct(x [, n])");
41 endif
42
43 realx = isreal(x);
44 transpose = (rows (x) == 1);
45
46 if transpose, x = x (:); endif
47 [nr, nc] = size (x);
48 if nargin == 1
49 n = nr;
50 elseif n > nr
51 x = [ x ; zeros(n-nr,nc) ];
52 elseif n < nr
53 x (n-nr+1 : n, :) = [];
54 endif
55
56 if ( realx && rem (n, 2) == 0 )
57 w = [ sqrt(n/4); sqrt(n/2)*exp((1i*pi/2/n)*[1:n-1]') ] * ones (1, nc);
58 y = ifft (w .* x);
59 y([1:2:n, n:-2:1], :) = 2*real(y);
60 elseif n == 1
61 y = x;
62 else
63 ## reverse the steps of dct using inverse operations
64 ## 1. undo post-fft scaling
65 w = [ sqrt(4*n); sqrt(2*n)*exp((1i*pi/2/n)*[1:n-1]') ] * ones (1, nc);
66 y = x.*w;
67
68 ## 2. reconstruct fft result and invert it
69 w = exp(-1i*pi*[n-1:-1:1]'/n) * ones(1,nc);
70 y = ifft ( [ y ; zeros(1,nc); y(n:-1:2,:).*w ] );
71
72 ## 3. keep only the original data; toss the reversed copy
73 y = y(1:n, :);
74 if (realx) y = real (y); endif
75 endif
76 if transpose, y = y.'; endif
77
78 endfunction