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Topic: Formula computing twiddle factors in FAAD (Read 2518 times) previous topic - next topic
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Formula computing twiddle factors in FAAD

In Libfaad in file mdct_tab.h are predefined twiddle factor, for example:
Code: [Select]
/* 256 (N/4) complex twiddle factors */
ALIGN static const complex_t mdct_tab_2048[] =
{
    { FRAC_CONST(0.031249997702054), FRAC_CONST(0.000011984224612) },
    { FRAC_CONST(0.031249813866531), FRAC_CONST(0.000107857810004) },
    { FRAC_CONST(0.031249335895858), FRAC_CONST(0.000203730380198) },


this constants after multiply by 32 is
Code: [Select]
    { FRAC_CONST(0.999999926465728), FRAC_CONST(0.000383495187584) },
    { FRAC_CONST(0.999994043728992), FRAC_CONST(0.003451449920128) },
    { FRAC_CONST(0.999978748667456), FRAC_CONST(0.006519372166336) },


But angles for sinus and cosinus are odd.
What is formula?

Formula computing twiddle factors in FAAD

Reply #1 –
Code: [Select]
    omega = 2.0f * M_PI / N;
    alpha = 2.0f * M_PI / (8.0f * N);
    
    for(n = 0; n < (N >> 2); ++n)
    {    
        twiddle[2*n] = (float) cos(omega * n + alpha);
        twiddle[2*n+1] = (float) sin(omega * n + alpha);
    }


Might need a scaling factor.
These are used pre and post fft (mdct implemented using fft).
"I hear it when I see it."

Formula computing twiddle factors in FAAD

Reply #2 –
I also found in mdct.c :
Quote
/* RE(mdct->sincos[k]) = scale*(real_t)(cos(2.0*M_PI*(k+1./8.) / (real_t)N));
    * IM(mdct->sincos[k]) = scale*(real_t)(sin(2.0*M_PI*(k+1./8.) / (real_t)N)); */
    /* scale is 1 for fixed point, sqrt(N) for floating point */

I correct sqrt(N) to sqrt(N/2) to be compatible with mdct_tab.h