Re: Pole-zero estimation from complex cepstrum

[Eckard Blumschein <Eckard.Blumschein@xxxxxxxxxxxxxxxxxxxxxxxxxx>]

> > Tarun Pruthi wrote:

> >> I am working on the automatic detection of vowel nasalization using
> >> knowledge-based acoustical parameters as part of my PhD thesis work.
...

> >> One of the techniuqes that I only got a short description about seemed to
> >> be very different. This was based on the complex cepstrum.

While Oppenheim and Schafer did not even consider the possibility that
real-valued  analysis of a single signal is absolutely equivalent to the
complex-valued one except for an arbitrarily chosen point of reference, I am not
aware of any reason for choosing complex cepstrum instead of real cepstrum. As
far as I know, just the real cepstrum has proven successful in practice for
decades.

Complex-valued spectrum in general has a lot of disadvantages. Above mentioned
reference merely relates to the arbitrarily choosen reference of time fixed at
midnight in Greenwich. Auditory function does not rely on this event-related
time scale. The auditory system does not know linear phase. Consequently complex
spectrum twice includes redundancy giving rise to ambiguity, confusion and
non-causal as well as possibly unstable behavior.

As long as one considers time extending from minus oo to plus oo, this
redundancy must not be omitted. However, if one considers elapsed time an always
only positive quantity, the volume of data reduces to just a quarter, and
spectrum simplifies without any loss of information. Most physicists merely
hesitate to abandon their unjustified believe in pre-existing future time.

Regards,
Eckard