That would also be my first choice. It might also be worth looking at modern algorithms in that family of methods. A lot of effort has gone into designing exponentially damped sine methods for voice compression and transmission. They will be more robust to noise than Prony's method. Some methods can even handle arbitrarily coloured noise, not just white. Some methods also deal with time-varying damped sinusoids, which would be interesting if your drums can change their resonant modes over time, as happens with the tabla, timpani and others.
Best, Ian On Sun, Jul 30, 2017 at 12:14 PM, Corey K <corey...@gmail.com> wrote: > You might want to look into a parametric method of estimating the partials > as well, e.g., Prony's method, which could give you much higher resolution > than the FFT. > > Best, > > Corey Kereliuk > www.reverberate.ca > > > On Jul 28, 2017 12:47 PM, "Thomas Rehaag" <develo...@netcologne.de> wrote: > > see below. > > >> ---------------------------- Original Message ---------------------------- >> Subject: Re: [music-dsp] tracking drum partials >> From: "Thomas Rehaag" <develo...@netcologne.de> >> Date: Thu, July 27, 2017 4:02 pm >> To: music-dsp@music.columbia.edu >> ------------------------------------------------------------ >> -------------- >> >> > >> > @Robert: >> > I didn't quite get "for analysis, i would recommend Gaussian windows >> > because each partial will have it's own gaussian bump in the frequency >> > domain ..." >> > Looks like you wouldn't just pick up the peaks like I do. >> > >> >> well, i *would* sorta, but it's not always as simple as that. >> >> ... >> >> >> > Next the highest peaks are taken from every FFT and then tracks in time >> > are built. >> > >> > And it looks like I've just found the simple key for better results >> > after putting the whole stuff aside for 3 weeks now. >> > It's just to use samples from drums that have been hit softly. >> > Else every bin of the first FFTs will be crossed by 2 or 3 sweeps which >> > leads to lots of artifacts. >> >> are you using MATLAB/Octave? you might need to think about fftshift() . >> >> suppose you have a sinusoid that goes on forever and you use a **very** >> long FFT and transform it. if you can imagine that very long FFT as >> approximating the Fourier Transform, you will get better than a "peak", you >> will get a *spike* and +/- f0, the frequency of that sinusoid (the >> "negative frequency" spike will be at N-f0). in the F.T., it's a pair >> dirac impulses at +/- f0. then when you multiply by a window in the time >> domain, that is convolving by the F.T. of the window in the frequency >> domain. i will call that F.T. of the window, the "window spectrum". a >> window function is normally a low-pass kinda signal, which means the window >> spectrum will peak at a frequency of 0. convolving that window spectrum >> with a dirac spike at f0 simply moves that window spectrum to f0. so it's >> no longer a spike, but a more rounded peak at f0. i will call that "more >> rounded peak" the "main lobe" of the window spectrum. and it is what i >> meant by the "gaussian bump" in the previous response. >> >> now most (actually all, to some degree) window spectra have sidelobes and >> much of what goes on with designing a good window function is to deal with >> those sidelobe bumps. because the sidelobe of one partial will add to the >> mainlobe of another partial and possibly skew the apparent peak location >> and peak height. one of the design goals behind the Hamming window was to >> beat down the sidelobes a little. a more systematic approach is the Kaiser >> window which allows you to trade off sidelobe height and mainlobe width. >> you would like *both* a skinny mainlobe and small sidelobes, but you can't >> get both without increasing the window length "L". >> >> another property that *some* windows have that are of interest to the >> music-dsp crowd is that of being (or not) complementary. that is adjacent >> windows add to 1. this is important in **synthesis** (say in the phase >> vocoder), but is not important in **analysis**. for example, the Kaiser >> window is not complementary, but the Hann window is. so, if you don't need >> complementary, then you might wanna choose a window with good sidelobe >> behavior. >> >> the reason i suggested Gaussian over Kaiser was just sorta knee-jerk. >> perhaps Kaiser would be better, but one good thing about the Gaussian is >> that its F.T. is also a Gaussian (and there are other cool properties >> related to chirp functions). a theoretical Gaussian window has no >> sidelobes. so, if you let your Gaussian window get extremely close to zero >> before it is truncated, then it's pretty close to a theoretical Gaussian >> and you need not worry about sidelobes and the behavior of the window >> spectrum is also nearly perfectly Gaussian and you can sometimes take >> advantage of that. like in interpolating around an apparent peak (at an >> integer FFT bin) to get the precise peak location. >> >> now you probably do not need to get this anal-retentive about it, but if >> you want to, you can look at this: >> https://www.researchgate.net/publication/3927319_Intraframe_ >> time-scaling_of_nonstationary_sinusoids_within_the_phase_vocoder >> and i might have some old MATLAB code to run for it, if you want it (or >> anyone else), lemme know. >> >> big thanks for the elaborate explanation! > Looks like you've turned my head into the right direction. > Had a look at the spectrum of my window: a 4096 Hann win. in the middle of > 64k samples. > A big sidelobe party! > A 64k gaussian window that just sets priority to an area of ~4096 samples > will of course fix that. > > Btw.: no Matlab here. C++ only. > > Best Regards, > > Thomas > > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp > > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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