Speex dev - Jan 2005 - autocorrelation and levinson-durbin

hi,

am trying to understand speex's algo.

have a few questions.
1) autocorrelation:
in the function, _spx_autocorr (for floating point
version), there is a line

ac[0] += 10;

correct me if i am wrong, i suppose the addition of 
10 is used to condition  the autocorrelation matrix.  
wonder how the value of 10 is arrived at?

2) levinson durbin (LD) algo
in the function _spx_lpc,

i referred to some LD algo online.  am puzzled with
the reflection coefficient's computation. from the code, i 
understand it to be

r = [- Rxx(i) - sum(lpc*Rxx)] / [error + 0.003* Rxx(0)]

first question is why is negative of Rxx(i) added?
from the resources i gather positive Rxx(i) is added.
second is what is the motivation behind adding
0.003*Rxx(0) to error?

3) a more general question:
i have not been able to find any reason why
10 lpcs are used.  i suppose 10 lpcs are 
enough for prediction and using more coeffs
would not have made too much difference.
and 10 is even, good for lpc->lsf. had read
somewhere "historically", during the analog 
era, this number is used.  or maybe 10 is analagous
to a perfect number! ;-) 

cheers,
tk

> have a few questions.
> 1) autocorrelation:
> in the function, _spx_autocorr (for floating point
> version), there is a line
> 
> ac[0] += 10;
> 
> correct me if i am wrong, i suppose the addition of 
> 10 is used to condition  the autocorrelation matrix.  
> wonder how the value of 10 is arrived at?
The value is indeed used to prevent unstable or boderline-stable
filters. The actual value isn't that important and was determined by
trial and error.
> 2) levinson durbin (LD) algo
> in the function _spx_lpc,
> 
> i referred to some LD algo online.  am puzzled with
> the reflection coefficient's computation. from the code, i 
> understand it to be
> 
> r = [- Rxx(i) - sum(lpc*Rxx)] / [error + 0.003* Rxx(0)]
> 
> first question is why is negative of Rxx(i) added?
No idea, I only modified an existing implementation.
> from the resources i gather positive Rxx(i) is added.
> second is what is the motivation behind adding
> 0.003*Rxx(0) to error?
Same as for 1). It's there so that a sine wave won't make the whole
thing unstable.
> 3) a more general question:
> i have not been able to find any reason why
> 10 lpcs are used.  i suppose 10 lpcs are 
> enough for prediction and using more coeffs
> would not have made too much difference.
> and 10 is even, good for lpc->lsf. had read
> somewhere "historically", during the analog 
> era, this number is used.  or maybe 10 is analagous
> to a perfect number! ;-) 
The more coefficients you have, the more you need to encode, 10 seemed
to be a good trade-off.

	Jean-Marc

-- 
Jean-Marc Valin <Jean-Marc.Valin@USherbrooke.ca>
Universit? de Sherbrooke