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
