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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Pole-zero estimation from complex cepstrum*From*: Tarun Pruthi <tpruthi@xxxxxxxxxxxx>*Date*: Fri, 12 May 2006 16:08:38 -0400*Comments*: To: Mark Hasegawa-Johnson <jhasegaw@uiuc.edu>*Delivery-date*: Fri May 12 16:18:15 2006*In-reply-to*: <4464B48A.6020904@uiuc.edu>*References*: <Pine.GSO.4.63.0605121117450.8068@y.glue.umd.edu> <4464B48A.6020904@uiuc.edu>*Reply-to*: Tarun Pruthi <tpruthi@xxxxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Hi 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].

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@xxxxxxxxxxxx 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@xxxxxxxxxxxx Web: www.ece.umd.edu/~tpruthi Ph: 301-405-1365 ----------------------------------------

**Follow-Ups**:**Re: Pole-zero estimation from complex cepstrum***From:*Eckard Blumschein

**References**:**Pole-zero estimation from complex cepstrum***From:*Tarun Pruthi

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