Subject: Re: Pole-zero estimation from complex cepstrum From: Tarun Pruthi <tpruthi@xxxxxxxx> Date: Fri, 12 May 2006 16:08:38 -0400Hi Mark, The equation that I am talking about goes like this: if v[n] = signal, V(z) = z transform of v[n] = N(z)/D(z), Vhat(z) = log V(z) then, -z*d(Vhat(z)) -z*V'(z) -z*(N'(z)*D(z) - N(z)*D'(z)) --------- = ---- = ------------------------ dz V(z) N(z)*D(z) -z*d(Vhat(z)) ifft ------------ <---> n*vhat[n] dz Therefore, the poles and zeros of v[n] become the pole of n*vhat[n]. The problem is that when I try to implement it in MATLAB it becomes unstable and gives some junk output. So, I wanted to find a more detailed reference for it (since this is all I know about it), and if possible a working code which can achieve this. With warm regards, Tarun On Fri, 12 May 2006, Mark Hasegawa-Johnson wrote: > Hi Tarun, > > Are you talking about equation 10.45 in Oppenheim & Schafer? > > - Mark > > Tarun Pruthi wrote: >> Hi all, >> >> I am working on the automatic detection of vowel nasalization using >> knowledge-based acoustical parameters as part of my PhD thesis work. In >> this context, I have looked at various techniques to estimate poles and >> zeros (eg. Shanks's method and various other techniques to linearize the >> zero estimation problem). Until now I haven't really found any technique >> that is very useful to locate the zeros in a nasal consonant/nasalized >> vowel spectrum. >> >> One of the techniuqes that I only got a short description about seemed to >> be very different. This was based on the complex cepstrum. In this >> technique a derivative of the log magnitude DFT spectrum is taken to >> effectively convert the zeros of a transfer function to poles and estimate >> their locations. Even though, the approach seems interesting I haven't been >> able to locate a detailed reference for this technique. >> >> I would be grateful if anyone could give me a reference for the paper, or >> the paper itself if possible. Also, if anyone has the code to implement it >> and is willing to share the code, please let me know. It would also be >> interesting to know your comments about the effectiveness of such pole-zero >> estimation techniques to the problem of locating zeros in the nasal >> consonant/nasalized vowel spectra. >> >> With warm regards, >> Tarun >> >> ----------------------------------------- >> Tarun Pruthi >> Graduate Research Assistant, ECE >> Room 3180, A V Williams Building >> University of Maryland, College Park >> MD 20742 USA >> Email: tpruthi@xxxxxxxx >> Web: www.ece.umd.edu/~tpruthi >> Ph: 301-405-1365 >> ---------------------------------------- >> >> >> > > ----------------------------------------- Tarun Pruthi Graduate Research Assistant, ECE Room 3180, A V Williams Building University of Maryland, College Park MD 20742 USA Email: tpruthi@xxxxxxxx Web: www.ece.umd.edu/~tpruthi Ph: 301-405-1365 ----------------------------------------