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copied!<p>I found a blog post that describes the integer based DCT and IDCT <a href="http://fgiesen.wordpress.com/2013/11/04/bink-2-2-integer-dct-design-part-1/" rel="nofollow">here</a> and gives an implementation in Matlab.</p> <p>The code he used is on GitHub, available <a href="https://github.com/rygorous/dct_blog" rel="nofollow">here</a>.</p> <p>I used the method bink_dct_B2.m. This calculates a scaled 1D-DCT transform, so if you want the 2D-orthogonal DCT tranform, you have have to use following code:</p> <pre><code>A_tranformed = (bink_dct_B2(bink_dct_B2(A)')')/8 </code></pre> <p>Here A is the matrix you want to transform. This will give approximately the same output as the Matlab built-in dct2-command (this integer implementation will introduce some rounding-errors).</p> <pre><code>function out=bink_dct_B2(in) % extract rows i0 = in(1,:); i1 = in(2,:); i2 = in(3,:); i3 = in(4,:); i4 = in(5,:); i5 = in(6,:); i6 = in(7,:); i7 = in(8,:); % stage 1 - 8A a0 = i0 + i7; a1 = i1 + i6; a2 = i2 + i5; a3 = i3 + i4; a4 = i0 - i7; a5 = i1 - i6; a6 = i2 - i5; a7 = i3 - i4; % even stage 2 - 4A b0 = a0 + a3; b1 = a1 + a2; b2 = a0 - a3; b3 = a1 - a2; % even stage 3 - 6A 4S c0 = b0 + b1; c1 = b0 - b1; c2 = b2 + b2/4 + b3/2; c3 = b2/2 - b3 - b3/4; % odd stage 2 - 12A 8S % NB a4/4 and a7/4 are each used twice, so this really is 8 shifts, not 10. b4 = a7/4 + a4 + a4/4 - a4/16; b7 = a4/4 - a7 - a7/4 + a7/16; b5 = a5 + a6 - a6/4 - a6/16; b6 = a6 - a5 + a5/4 + a5/16; % odd stage 3 - 4A c4 = b4 + b5; c5 = b4 - b5; c6 = b6 + b7; c7 = b6 - b7; % odd stage 4 - 2A d4 = c4; d5 = c5 + c7; d6 = c5 - c7; d7 = c6; % permute/output out = [c0; d4; c2; d6; c1; d5; c3; d7]; % total: 36A 12S end </code></pre>

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