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Re: All pole LPC filter again

Started by Bhanu Prakash May 6, 2002
Hi,

All the reasonings given for 10th order LPC is plausible. But i encountered
50th order filter
in G.728(LD-CELP). what could be the probable reason for having such a high
order
(computationally intensive) LPC in this codec.

Note: The codec is a backward adaptive and uses 20 sample frame(2.5msec).

Best Regards,
BhanuPrakash ----- Original Message -----
From: "Sameer Kibey" <>
To: <>
Sent: Sunday, May 05, 2002 9:14 PM
Subject: [speechcoding] All pole LPC filter again > Hi all !
>
> To understand whether the all pole LPC filter model
> 'ignores' the zeros or not, let us see a few points
> mentioned in the book "Digital Processing of Speech
> Signals" by Rabiner & Schafer:
>
> 1. "An all ploe model is a very good representation of
> the vocal tract effects for a majority of speech
> sounds ; however the acoustic theory tells us that
> NASALS and FRICATIVES require both resonances and
> antiresonances (poles and zeros)."
>
> 2."In these cases we may include zeros in the transfer
> funtion or we may use the fact that effect of zero of
> the transfer function can be achieved by including
> more poles." (See page 99).
>
> 3. As a proof of the above statement, the reader is
> asked to refer to the Problem 3.10 on page 112, which
> i shall repeat here :
>
> "Show that if |a| < 1,
>
> 1-a*z^(-1) = 1/(summation(a^n * z^(-n))), where n goes
> from 0 to infinity
>
> and thus, that a zero can be approximated as closely
> as desired by multiple poles."
>
> The above equation can be easily proved using the
> formula for sum of N terms of a geometric series ( the
> denominator of the RHS is a geometric series).
>
> Hence, if i may say so again, the all pole model does
> not "ignore" the zeros, but "compensates" for them but
> adding 2 more poles.
>
> Any more comments?
> Sameer.
> p.s : examples of nasals are the sounds like /m/,/n/
> where the vocal tract is totally constricted at some
> point along the oral cavity and air flows thro' the
> nasal tract.Similarly for the fricatives like /s/,
> /z/,/sh/,/f/ there is formation of constriction along
> the vocal tract which calls for the antiresonance
> effect.
>
> > Actually the 2 poles, which do not exactly
> > correspond to the formants, are
> > real poles that corresponds to usually the
> > frequencies at 0 and Fs/2. Thus
> > we use 10 poles, 4 pairs of complex conjugate poles
> > and 2 real poles. I dont
> > think the 2 poles are for compensating the zeros.
> > Its just that any zero can
> > be represented by poles. For eg. the first order
> > polynomial 1-x is
> > approximately equivalent to 1/(1+x).
> >
> > Hope this answers your question.
> >
> > Cheers
> > -Hari
> >
> >
>
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