>Sinc interpolation would be theoretically correct, but, remember, >that this thread is not about "strictily theoretically correct" frequency >recognition, but rather about some "more intuitive" version with the >concept of "instant frequency".
What is "instant frequency?" I have to say that I find this concept to be highly counter-intuitive on its face. How can we speak meaningfully about frequency on time scales shorter than one period? >Maybe we could attempt exactly fitting a set of samples into a sum >of sines of different frequencies? Each sine corresponding to 3 degrees >of freedom. Yeah, this is called sinusoidal modeling. But I don't see how it give you any handle on "instantaneous frequency." If you're operating on time scales shorter than the periods of the frequencies in question, then the basis functions you're using in sinusoidal modeling do not exhibit any meaningful periodicity, but instead look something like low-order polynomials. The frequency parameters you'd estimate would be meaningless as such - they'd jump around all over the place from frame to frame, depending on exactly how the frame being analyzed lined up with the basis functions. I.e., they'd just be abstract parameters specifying some low-order-polynomial-ish shapes, and not indicating anything meaningful about periodicity. The only way I can see to speak meaningfully about instantaneous frequency is if you were to decompose a signal with some kind of chirp basis - on a time scale much longer than any particular period seen in the chirp basis. Then you could turn around and say that the frequency is evolving according to the chirp parameter, and talk about an instantaneous frequency at any particular time. But not that this requires doing the analysis on a rather *long* time scale, so you can be confident that the chirp structure you're finding actually corresponds to some real signal content. E On Thu, Jul 17, 2014 at 1:30 AM, Vadim Zavalishin < vadim.zavalis...@native-instruments.de> wrote: > On 16-Jul-14 15:29, Olli Niemitalo wrote: > >> Not sure if this is related, but there appears to be something called >> "chromatic derivatives": >> >> http://www.cse.unsw.edu.au/~ignjat/diff/ >> > > Seems pretty much related and going further in the same direction > (alright, I just briefly glanced at chromatic derivatives). Anyway, it > seems that for the discrete time signals the situation is somewhat > different from what I described for continuous time in that there are no > derivative discontinuities for discrete time signals. At the same time it's > not possible to locally compute the derivatives of the discrete time > signals, so the local Taylor expansion idea is not applicable anyway (the > same applies to the the chromatic derivatives, I'd guess). However, > instead, we could simply apply the inter-/extra-polation to the obtained > sample points. The most intuitive would be applying Lagrange interpolation, > which as we know, converges to the sinc interpolation. However (again, > remember the BLEP discussion), any finite order polynomial contains only > the generalized DC component. Not very useful for the frequency estimation. > So, the question is, what kind of interpolation should we use? Sinc > interpolation would be theoretically correct, but, remember, that this > thread is not about "strictily theoretically correct" frequency > recognition, but rather about some "more intuitive" version with the > concept of "instant frequency". Maybe we could attempt exactly fitting a > set of samples into a sum of sines of different frequencies? Each sine > corresponding to 3 degrees of freedom. > > > Regards, > Vadim > > -- > Vadim Zavalishin > Reaktor Application Architect > Native Instruments GmbH > +49-30-611035-0 > > www.native-instruments.com > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, > dsp links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp > -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
