# Re: About importance of "phase" in sound recognition

In that case let me give another example: the impulse response of a gammatone filter (with some specific parameters) is something like (t in arbitrary units but positive):

t * exp(-t) * cos(w*t+phi)

This signal definitely has an onset, and (arguably?) has a meaningful phase -- meaningful in the sense that a sentence like 'shifting the phase of this signal' makes sense.

I think that the distinction between signals which have or do not have phase is not binary - it is a gradual transition between the two, since the question 'when is a signal (semi) periodic?' does not have one answer, not mathematically and not psychoanalytically - A sinosuid of .5 a period is clearly not periodic, but a sinosuid of 100 periods clearly is - where is the transition between the 'periodic' and 'non-periodic'? it is not a point-transition.

On Thu, Oct 7, 2010 at 1:37 PM, Laszlo Toth wrote:
On Thu, 7 Oct 2010, ita katz wrote:

> A delta function can be built from a linear combination of periodic signals,
> and it is definitely a signal 'with onset'.

I that case each component will have its own phase, but the sum (the delta
function) has no phase, because it is not periodic. So my point was that
while it makes sense to talk about the phase of (periodic!!) components,
you should be careful when talking about the phase of a complex. Many
people are willing to forget about it.

> Or, In the same spirit, an onset can be periodically-extended by repeating
> it infinitely into the past and the future,

Yes, and it turns it into a periodic function, which does have phase.
But it no longer has an onset, as it extends infinitely into the past...

> and then it can be represented  as a sum of countable (possibly
> infinite) number of periodic components.

Again, I wasn't talking about its components, I was talking about the
signal itself.

Laszlo Toth