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# Re: Pole-zero estimation from complex cepstrum

`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].`

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@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
----------------------------------------```