� thanks Steffan. i am looking cursorily�at the paper. �about 15 years ago i did some work in sinusoidal modeling and noticed a useful feature of the Gaussian: that the Fourier transform of a gaussian is time domain is a gaussian in the frequency domain. � and similarly for a linearly-swept frequency chirp. �and the similarity between the gaussian and the chirp. they are both e^(-a t^2), but for the chirp the "a" factor might have a "j" or an "i" in it. i got some nice results for how, using a gaussian window, you can extract the frequency, the sweep rate on the frequency, and the ramp rate on the amplitude of a sinusoidal chirp. �it's in an IEEE WASPAA (Mohonk) paper from 2001. �http://ieeexplore.ieee.org/document/969581/� you might get a free copy at �https://www.researchgate.net/publication/3927319_Intraframe_time-scaling_of_nonstationary_sinusoids_within_the_phase_vocoder� if the researchgate doesn't get you the doc, lemme know and i will email it to you. anyway, i want to make one observation regarding the CERN paper and the parabolic interpolation to find the "true" peak from the discrete peak and the two neighboring points. �while it is true that when using parabolic or quadratic interpolation on the *magnitude* or *magnitude-squared* can result in some small error (and different window functions may be compared), there is no theoretical error if you're using a gaussian window *and* you are observing the logarithm of magnitude. �using a gaussian window in the time domain results in a gaussian function in the frequency domain for a single sinusoid. �and in the log-magnitude domain, the curve is precisely a quadratic, so the 3-point interpolation works perfectly well in that case. �perhaps the CERN paper says that also, but it looked like they were comparing this interpolation error in the not-logged magnitude given a few different windows. -- r b-j � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge." ---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] Recognizing Frequency Components From: "STEFFAN DIEDRICHSEN" <sdiedrich...@me.com> Date: Fri, January 27, 2017 6:32 am To: r...@audioimagination.com music-dsp@music.columbia.edu -------------------------------------------------------------------------- > Here it is from our nuclear friends at CERN: > > https://mgasior.web.cern.ch/mgasior/pap/FFT_resol_note.pdf > <https://mgasior.web.cern.ch/mgasior/pap/FFT_resol_note.pdf> > > > Steffan > > > >> On 26.01.2017|KW4, at 20:01, robert bristow-johnson >> <r...@audioimagination.com> wrote: >> >> i thought Steffan mentioned something about using a Gaussian window. he >> mentioned a paper he found but did not identify it. i am a little curious. >> >> > >
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