Subject: Re: About importance of "phase" in sound recognition From: ita katz <itakatz@xxxxxxxx> Date: Thu, 7 Oct 2010 13:56:10 +0200 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--002215046aff7b62a5049205941a Content-Type: text/plain; charset=ISO-8859-1 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 <tothl@xxxxxxxx> 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 > Hungarian Academy of Sciences * > Research Group on Artificial Intelligence * "Failure only begins > e-mail: tothl@xxxxxxxx * when you stop trying" > http://www.inf.u-szeged.hu/~tothl<http://www.inf.u-szeged.hu/%7Etothl> * > > --002215046aff7b62a5049205941a Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr">In that case let me give another example: the impulse resp= onse of a gammatone filter (with some specific parameters) is something lik= e (t in arbitrary units but positive):<br><div style=3D"margin-left: 40px;"= > <br>t * exp(-t) * cos(w*t+phi)<br></div><br>This signal definitely has an o= nset, and (arguably?) has a meaningful phase -- meaningful in the sense tha= t a sentence like 'shifting the phase of this signal' makes sense. = <br> <br>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 ans= wer, not mathematically and not psychoanalytically - A sinosuid of .5 a per= iod is clearly not periodic, but a sinosuid of 100 periods clearly is - whe= re is the transition between the 'periodic' and 'non-periodic&#= 39;? it is not a point-transition. <br> <div><br><div><br><div class=3D"gmail_quote">On Thu, Oct 7, 2010 at 1:37 PM= , Laszlo Toth <span dir=3D"ltr"><<a href=3D"mailto:tothl@xxxxxxxx= ">tothl@xxxxxxxx</a>></span> wrote:<br><blockquote class=3D"gmail= _quote" style=3D"margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204,= 204, 204); padding-left: 1ex;"> On Thu, 7 Oct 2010, ita katz wrote:<br> <br> > A delta function can be built from a linear combination of periodic si= gnals,<br> > and it is definitely a signal 'with onset'.<br> <br> I that case each component will have its own phase, but the sum (the delta<= br> function) has no phase, because it is not periodic. So my point was that<br= > while it makes sense to talk about the phase of (periodic!!) components,<br= > you should be careful when talking about the phase of a complex. Many<br> people are willing to forget about it.<br> <br> > Or, In the same spirit, an onset can be periodically-extended by repea= ting<br> > it infinitely into the past and the future,<br> <br> Yes, and it turns it into a periodic function, which does have phase.<br> But it no longer has an onset, as it extends infinitely into the past...<br= > <br> > and then it can be represented =A0as a sum of countable (possibly<br> > infinite) number of periodic components.<br> <br> Again, I wasn't talking about its components, I was talking about the<b= r> signal itself.<br> <font color=3D"#888888"><br> =A0 =A0 =A0 =A0 =A0 =A0 =A0 Laszlo Toth<br> =A0 =A0 =A0 =A0Hungarian Academy of Sciences =A0 =A0 =A0 =A0 *<br> =A0Research Group on Artificial Intelligence =A0 * =A0 "Failure only = begins<br> =A0 =A0 e-mail: <a href=3D"mailto:tothl@xxxxxxxx">tothl@xxxxxxxx= d.hu</a> =A0 =A0 =A0 =A0 =A0 =A0* =A0 =A0when you stop trying"<br> =A0 =A0 <a href=3D"http://www.inf.u-szeged.hu/%7Etothl" target=3D"_blank">= http://www.inf.u-szeged.hu/~tothl</a> =A0 =A0 =A0 =A0*<br> <br> </font></blockquote></div><br></div></div></div> --002215046aff7b62a5049205941a--