Re: Pole-zero estimation from complex cepstrum

[Tarun Pruthi <tpruthi@xxxxxxxxxxxx>]

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
----------------------------------------