Hi, All the reasonings given for 10th order LPC is plausible. But i encountered 50th order filter in G.728(LDCELP). 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, > > 1a*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 1x is > > approximately equivalent to 1/(1+x). > > > > Hope this answers your question. > > > > Cheers > > Hari > > > > > > __________________________________________________ > > > _____________________________________ > Note: If you do a simple "reply" with your email client, only the author of this message will receive your answer. You need to do a "reply all" if you want your answer to be distributed to the entire group. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/speechcoding > > Other DSPRelated Groups: http://www.dsprelated.com > ">http://docs.yahoo.com/info/terms/ 
