---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] Recognizing Frequency Components From: "Nigel Redmon" <earle...@earlevel.com> Date: Sat, January 28, 2017 2:38 pm To: "A discussion list for music-related DSP" <music-dsp@music.columbia.edu> -------------------------------------------------------------------------- >> Always fun to extrapolate into the blue, huh ? Not so much > > I think people participate because they enjoy discussing audio DSP topics, so > things often diverge from the original question—this isn’t simply > an answer forum. > well, it was when Steffan mentioned "gaussian window" in the context of finding this parameter called "frequency", given a bunch of samples. gaussian windows are tits because gaussian functions are really cool for a variety of reasons. >> I read only a part fo the RBJ "From zero to first order principal component >> synthesis" article yet, but am aware that, just like some other >> generalizations, drawing from general mathematics of the last century all >> too enthusiastically > > > Published on only the second month of the current century, I’d expect > Robert’s paper to draw enthusiastically on the last century ;-) > > Having trouble parsing that last paragraph, please excuse me if I > misinterpreted. > i can't always figure out what Theo is saying either. i don't think of this in the context of which century. �more of an example of the parameter extraction problem that they teach us about in grad school. �the approach *was* to extract the parameters out of the frequency-domain data. �i s'pose you can do a brute-force approach in the time domain and posit a slew of sinusoids with different frequencies. �for each proposed frequency, it is pretty straight forward to extract the amplitude and phase of a sinusoid of that frequency that has the least-mean-square error (you get the amplitudes on the cosine and sine component). you do that for each proposed frequency and pick the frequency that has the smallest mean-square error. �then maybe do some searching around that "best" frequency to find an even better frequency that is close by. the sinusoidal modeling proposed in the paper essentially can come to a best guess of the frequency (and the sweep rate and the amplitude ramp rate) without trial-and-error searching. �it chooses those three parameters in such a way to best match the quadratic exponent of the gaussian pulse in the frequency domain that each sinusoid will leave. �that's what it's for. �then, i s'pose, you can get the amplitude and the phase of the chirpy sinusoid similar as before now that you have a frequency to work with. �then you have a full description of the sinusoid (to the extent of its frequency and sweep and ramp rates, but not higher-order terms) that you can use in modification and reconstruction. -- r b-j � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge."
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