opus/libcelt/mdct.c

/* (C) 2008 Jean-Marc Valin, CSIRO
*/
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*/

/* This is a simple MDCT implementation that uses a N/4 complex FFT
   to do most of the work. It should be relatively straightforward to
   plug in pretty much and FFT here.
   
   This replaces the Vorbis FFT (and uses the exact same API), which 
   was a bit too messy and that was ending up duplicating code 
   (might as well use the same FFT everywhere).
   
   The algorithm is similar to (and inspired from) Fabrice Bellard's
   MDCT implementation in FFMPEG, but has differences in signs, ordering
   and scaling in many places. 
*/

#include "mdct.h"
#include "kiss_fft.h"
#include <math.h>
#include "os_support.h"

#ifndef M_PI
#define M_PI 3.14159263
#endif

void mdct_init(mdct_lookup *l,int N)
{
   int i;
   int N2, N4;
   l->n = N;
   N2 = N/2;
   N4 = N/4;
   l->kfft = kiss_fft_alloc(N4, NULL, NULL);
   l->trig = celt_alloc(N2*sizeof(float));
   /* We have enough points that sine isn't necessary */
   for (i=0;i<N2;i++)
      l->trig[i] = cos(2*M_PI*(i+1./8.)/N);
   l->scale = 1./N4;
}

void mdct_clear(mdct_lookup *l)
{
   kiss_fft_free(l->kfft);
   celt_free(l->trig);
}

void mdct_forward(mdct_lookup *l, float *in, float *out)
{
   int i;
   int N, N2, N4, N8;
   N = l->n;
   N2 = N/2;
   N4 = N/4;
   N8 = N/8;
   float f[N2];
   
   /* Consider the input to be compused of four blocks: [a, b, c, d] */
   /* Shuffle, fold, pre-rotate (part 1) */
   for(i=0;i<N8;i++)
   {
      float re, im;
      /* Real part arranged as -d-cR, Imag part arranged as -b+aR*/
      re = -in[N2+N4+2*i] - in[N2+N4-2*i-1];
      im = -in[N4+2*i]    + in[N4-2*i-1];
      out[2*i]   = re*l->trig[i]  -  im*l->trig[i+N4];
      out[2*i+1] = im*l->trig[i]  +  re*l->trig[i+N4];
   }
   for(;i<N4;i++)
   {
      float re, im;
      /* Real part arranged as a-bR, Imag part arranged as -c-dR */
      re =   in[2*i-N4] - in[N2+N4-2*i-1];
      im = -(in[N4+2*i] + in[N+N4-2*i-1]);
      out[2*i]   = re*l->trig[i]  -  im*l->trig[i+N4];
      out[2*i+1] = im*l->trig[i]  +  re*l->trig[i+N4];
   }

   /* N/4 complex FFT, which should normally down-scale by 4/N (but doesn't now) */
   kiss_fft(l->kfft, (const kiss_fft_cpx *)out, (kiss_fft_cpx *)f);

   /* Post-rotate and apply the scaling if the FFT doesn't to it itself */
   for(i=0;i<N4;i++)
   {
      out[2*i]      = l->scale * (-f[2*i+1]*l->trig[i+N4] + f[2*i]  *l->trig[i]);
      out[N2-1-2*i] = l->scale * (-f[2*i]  *l->trig[i+N4] - f[2*i+1]*l->trig[i]);
   }
}


void mdct_backward(mdct_lookup *l, float *in, float *out)
{
   int i;
   int N, N2, N4, N8;
   N = l->n;
   N2 = N/2;
   N4 = N/4;
   N8 = N/8;
   float f[N2];
   
   /* Pre-rotate */
   for(i=0;i<N4;i++) 
   {
      out[2*i]   = -in[N2-2*i-1] * l->trig[i]    - in[2*i]*l->trig[i+N4];
      out[2*i+1] =  in[N2-2*i-1] * l->trig[i+N4] - in[2*i]*l->trig[i];
   }

   /* Inverse N/4 complex FFT. This one should *not* downscale even in fixed-point */
   kiss_ifft(l->kfft, (const kiss_fft_cpx *)out, (kiss_fft_cpx *)f);
   
   /* Post-rotate */
   for(i=0;i<N4;i++)
   {
      float re, im;
      re = f[2*i];
      im = f[2*i+1];
      f[2*i]   = re*l->trig[i] + im*l->trig[i+N4];
      f[2*i+1] = im*l->trig[i] - re*l->trig[i+N4];
   }
   /* De-shuffle the components for the middle of the window only */
   for(i = 0; i < N4; i++)
   {
      out[N4+2*i]   =-f[2*i];
      out[N4+2*i+1] = f[N2-2*i-1];
   }

   /* Mirror on both sides for TDAC */
   for(i = 0; i < N4; i++)
   {
      out[i]     =-out[N2-i-1];
      out[N-i-1] = out[N2+i];
   }
}