# Re: A new paradigm?(On pitch and periodicity (was "correction to post"))

```Hi Ranjit,

In respect of the paragraph below, what you're suggesting is essentially the same as the Teager energy operator. I applied a "stabilised" form of this idea to the output of an auditory filter-bank, loosely based on a very early version of Dick Lyon's auditory model, in the late 1980s. I extended it to include estimates of the signal energy, the phase velocity of the travelling wave within the cochlea (analogous to Yegnanarayana's "modified group delay"), and the dominant frequency at each point along the basilar membrane. There are some examples of these parameters in this paper:

http://stevebeet.supanet.com/assets/archives/IOA92.zip

and a more detailed description of the analysis method is in this one (I don't have an electronic copy for this I'm afraid):

"Automatic speech recognition using a reduced auditory representation and position-tolerant discrimination. S. W. Beet. Computer Speech and Language, Vol. 4, pp 17-33. January 1990."

It might be worth taking a look at these before trying your ideas out - the presence of the dx(t)/dt term in your equation will make any results very susceptible to background noise and distortion unless you take some measures akin to those described in the Computer Speech and Language paper.

Steve Beet

On Tue, 6 Sep 2011 12:53:12 -0400
Ranjit Randhawa <rsran@xxxxxxxxxxx> wrote:

> If one were to consider a pure sinusoid in the phase domain (one where
> the axis are x(t) and dx(t)/dt), the locus would be a circle. The area
> of this circle would give us the magnitude, though how to determine this
> requires a different approach as the integration over 2pi would be zero.
> If we consider the product x(t)*dx(t)/dt as the rate of change of energy
> it would have a sign associated with it, then it is possible to
> determine this area, though the resulting algorithm would be too simple
> and fall apart for more complex signals since we don't know the period.
```