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POHow does this implementation of 1D IDCT work?
 

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  1. POHow does this implementation of 1D IDCT work?
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    <p>I have an implementation of a Inverse Discrete Cosine Transform and I'm trying to figure out how they got to this code. So far, I've figured out that this is probably an optimized implementation of the <a href="http://cnx.org/content/m12016/latest/" rel="nofollow">Cooley-Tukey radix-2 Decimation-in-time</a> for a DCT instead of a DFT (Discrete Fourier Transform).</p> <p>However, I'm still at a loss about exactly what happens at each stage. I figured that the Wx constants are probably the twiddle factors.</p> <p>Can anybody provide a reference to an explanation, or provide some explanation to this code? </p> <pre><code>//Twiddle factors #define W1 2841 /* 2048*sqrt(2)*cos(1*pi/16) */ #define W2 2676 /* 2048*sqrt(2)*cos(2*pi/16) */ #define W3 2408 /* 2048*sqrt(2)*cos(3*pi/16) */ #define W5 1609 /* 2048*sqrt(2)*cos(5*pi/16) */ #define W6 1108 /* 2048*sqrt(2)*cos(6*pi/16) */ #define W7 565 /* 2048*sqrt(2)*cos(7*pi/16) */ //Discrete Cosine Transform on a row of 8 DCT coefficients. NJ_INLINE void njRowIDCT(int* blk) { int x0, x1, x2, x3, x4, x5, x6, x7, x8; int t; if (!((x1 = blk[4] &lt;&lt; 11) | (x2 = blk[6]) | (x3 = blk[2]) | (x4 = blk[1]) | (x5 = blk[7]) | (x6 = blk[5]) | (x7 = blk[3]))) { blk[0] = blk[1] = blk[2] = blk[3] = blk[4] = blk[5] = blk[6] = blk[7] = blk[0] &lt;&lt; 3; return; } x0 = (blk[0] &lt;&lt; 11) + 128; //For rounding at fourth stage //First stage /*What exactly are we doing here? Do the x values have a meaning?*/ x8 = W7 * (x4 + x5); x4 = x8 + (W1 - W7) * x4; x5 = x8 - (W1 + W7) * x5; x8 = W3 * (x6 + x7); x6 = x8 - (W3 - W5) * x6; x7 = x8 - (W3 + W5) * x7; //Second stage x8 = x0 + x1; x0 -= x1; x1 = W6 * (x3 + x2); x2 = x1 - (W2 + W6) * x2; x3 = x1 + (W2 - W6) * x3; x1 = x4 + x6; x4 -= x6; x6 = x5 + x7; x5 -= x7; //Third stage x7 = x8 + x3; x8 -= x3; x3 = x0 + x2; x0 -= x2; x2 = (181 * (x4 + x5) + 128) &gt;&gt; 8; x4 = (181 * (x4 - x5) + 128) &gt;&gt; 8; //Fourth stage blk[0] = (x7 + x1) &gt;&gt; 8; //bit shift is to emulate 8 bit fixed point precision blk[1] = (x3 + x2) &gt;&gt; 8; blk[2] = (x0 + x4) &gt;&gt; 8; blk[3] = (x8 + x6) &gt;&gt; 8; blk[4] = (x8 - x6) &gt;&gt; 8; blk[5] = (x0 - x4) &gt;&gt; 8; blk[6] = (x3 - x2) &gt;&gt; 8; blk[7] = (x7 - x1) &gt;&gt; 8; } </code></pre>
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    1. COBeautiful! I love algorithmic code, who needs obfuscators when you have this.
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