hi music-dsp, just a disclosure that I worked on this whilst studying for my master's degree at NYU, and was also a summer intern at Eventide. incidentally, one of the founders at Eventide, John Agnello, has a patent that is similar to what is being discussed here.
https://patents.justia.com/patent/5228093 best wishes, z eric zhang PS - does anyone know if Dan Gillespie from Columbia is on this list? On Sat, Mar 21, 2020 at 3:55 AM Andreas Gustafsson <g...@waxingwave.com> wrote: > robert bristow-johnson wrote: > > i've also fiddled with Gaussian windows and STFT around the turn of > > the century. i like that the Fourier Transform of a Gaussian is > > another Gaussian, so each frequency component will generate a > > Gaussian pulse in the frequency domain. > > Yes. The Gaussian also has many other nice properties such as being > free of side lobes, having faster than exponential fall-off, and being > both separable and circularly symmetric in the 2-D case. > > > how many of these do you have per octave, Andreas? looks like it > > could be 24 or 48. > > The demos use 48 frequency bands per octave, but the underlying > library can handle any integer number of bands per octave from 6 > up to several hundred. > > > does this make the pixel density along the t-axis be the same for > > higher octaves as it is for lower? because for constant-Q, you can > > have more pixels per second for the high pitched bins. but drawing > > that would be a little weird. > > There's a distinction between spectrogram coefficients (filter bank > output samples) and display pixels. The density of the coefficients > along the time axis is indeed higher in the higher octaves. > > Converting the coefficients to display pixels involves taking their > magnitudes and then resampling the magnitudes to the density of pixels > per time unit implied by the display zoom factor. This means > different octaves get resampled by different factors; typically an > octave somewhere in the middle ends up with a one-to-one > correspondence between coefficients and pixels, while higher octaves > are decimated and lower octaves are interpolated. > > > which is sorta the wavelet thing. > > Yes, that is one way of looking at it. > > > Andreas, for each pixel, what parameters do you have? like an > > amplitude and phase, or do you have more data such as frequency > > sweep rate or amplitude ramp rate? Using a Gaussian window, you can > > extract all that data out of the windowed samples that are used for > > the pixel. > > Again distinguishing between coefficients and pixels, the coefficients > of each frequency band are just complex quadrature samples of the > band's signal downmixed to baseband (using radio terminology), so to > determine the sweep rate or amplitude ramp rate you have to look at > more than one coefficient. > > In the displayed pixels, the only parameter is the magnitude; the > phase has been discarded (and therefore the original signal can only > be reconstructed from the coefficients, not from the pixels). The > coloring in the demo is made by constructing a separate spectrogram > for each stereo channel or track, tinting them differently and adding > them together in RGB space. > -- > Andreas Gustafsson, g...@waxingwave.com > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp > >
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