Hydrogenaudio Forums > Question about MDCT pre/post rotation

Mike Giacomelli

Jul 8 2007, 17:52

Going over the ffmpeg MDCT code, I noticed that the phase of each sin and cos term has a constant added to it.

QUOTE

/**
* init MDCT or IMDCT computation.
*/
int ff_mdct_init(MDCTContext *s, int nbits, int inverse)
{
int n, n4, i;
float alpha;

memset(s, 0, sizeof(*s));
n = 1 << nbits;
s->nbits = nbits;
s->n = n;
n4 = n >> 2;
s->tcos = av_malloc(n4 * sizeof(FFTSample));
if (!s->tcos)
goto fail;
s->tsin = av_malloc(n4 * sizeof(FFTSample));
if (!s->tsin)
goto fail;

for(i=0;i<n4;i++) {
alpha = 2 * M_PI * (i + 1 / 8.0) / n;
s->tcos[i] = -cos(alpha);
s->tsin[i] = -sin(alpha);
}

http://svn.mplayerhq.hu/ffmpeg/trunk/libav...t.c?view=markup

The bolded line is what I don't understand. Why is the constant 0.125 added to each phase term ? It seems to advance the phase by 2*pi divided by 8 times the block size, but i have no idea why.

Mike Giacomelli

Jul 9 2007, 08:25

I looked into this a little more, and FAAD also uses the 1/8 phase constant it for it's MDCT computation. I've tried decoding a file with the constant removed and I couldn't hear a difference (though the values changed in the last 3 or so bits).

Anyone know why its there?

Mike Giacomelli

Jul 10 2007, 08:56

Maybe that question was too specific. Could someone provide me with a good reference on the MDCT so I can determine the answer myself?

Woodinville

Jul 11 2007, 15:52

QUOTE(Mike Giacomelli @ Jul 10 2007, 07:56)

Maybe that question was too specific. Could someone provide me with a good reference on the MDCT so I can determine the answer myself?

Malvar's book on Transforms.

jido

Jul 11 2007, 17:16

QUOTE(Mike Giacomelli @ Jul 9 2007, 06:25)

I looked into this a little more, and FAAD also uses the 1/8 phase constant it for it's MDCT computation. I've tried decoding a file with the constant removed and I couldn't hear a difference (though the values changed in the last 3 or so bits).

Anyone know why its there?

Just a guess, but do you get an error for some input data with the constant removed? Like division by zero or such...

mc calculust

Oct 19 2007, 14:55

QUOTE(Mike Giacomelli @ Jul 8 2007, 17:52)

Going over the ffmpeg MDCT code, I noticed that the phase of each sin and cos term has a constant added to it.

QUOTE

/**
* init MDCT or IMDCT computation.
*/
int ff_mdct_init(MDCTContext *s, int nbits, int inverse)
{
int n, n4, i;
float alpha;

memset(s, 0, sizeof(*s));
n = 1 << nbits;
s->nbits = nbits;
s->n = n;
n4 = n >> 2;
s->tcos = av_malloc(n4 * sizeof(FFTSample));
if (!s->tcos)
goto fail;
s->tsin = av_malloc(n4 * sizeof(FFTSample));
if (!s->tsin)
goto fail;

for(i=0;i<n4;i++) {
alpha = 2 * M_PI * (i + 1 / 8.0) / n;
s->tcos[i] = -cos(alpha);
s->tsin[i] = -sin(alpha);
}

http://svn.mplayerhq.hu/ffmpeg/trunk/libav...t.c?view=markup

The bolded line is what I don't understand. Why is the constant 0.125 added to each phase term ? It seems to advance the phase by 2*pi divided by 8 times the block size, but i have no idea why.

The answer to this is probably really detailed mathematically. I would guess that it is the phase term used for Time Domain Aliasing Cancellation. The derivation of the fast MDCT can get really complicated, so it's hard to say!

Garf

Dec 21 2007, 09:55

There is a derivation in:

P. Duhamel, Y. Mahieux, and J. Petit, “A Fast Algorithm For
The Implementation Of Filterbanks Based On “Time Domain Aliasing
Cancellation””, Proceedings of the IEEE International Conference on
Acoustics, Speech, and Signal Processing, pp. 2209–2212, May 1991.