Re: Sound Analysis Tools ("Julius O. Smith III" )

Subject: Re: Sound Analysis Tools
From:    "Julius O. Smith III"  <jos(at)CCRMA.STANFORD.EDU>
Date:    Fri, 17 Nov 1995 11:19:41 -0800

> > Since the Fourier transform is linear, the two are equivalent. > > As the Fourier transform is windowed, there is always a time/frequency > resolution tradeoff. So, the interpolation is not as accurate as one > wants. In the time domain, band-limited interpolation is ideal. In the frequency domain, time-limited interpolation is ideal, since a window was used in the time domain. In my experience, interpolation is generally about the same amount of work in either case, per sample. However, since a spectral peak is more localized in the frequency domain, it is obviously less work to interpolate the window-transform main lobe than it is to interpolate the whole windowed sinusoid in the time domain. Anyway, my only point was that in principle subtraction in the time and freq domains are equivalent, ignoring sampling details. > I think that the gaussian is the easiest window to interpret as its > transform is a... gaussian. We also like the Gaussian window because its transform is a parabola on a dB scale and so it is exactly interpolated by quadratic interpolation in the frequency domain. However, the Gaussian window must itself be windowed, so results are not exact. What window do you use on the Gaussian window? Have you quantified the resulting interpolation error? Thanks, Julius

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