>*my* point is that as the delay slowly slides from a integer number of samples, where the transfer function is > > H(z) = z^-N > >to the integer + 1/2 sample (with gain above), this linear but time-variant system is going to sound like there is a LPF getting segued in. > >this, for me, is enough to decide never to use solely linear interpolation for a modulateable delay widget. if i vary delay, i want only the >delay to change.
Yeah, absolutely. The variable suppression of high frequencies when fractional delay changes is undesirable, and indicates that better interpolation schemes should be used there. But the example of the weird things that can happen when you try to sample a sine wave right at the nyquist rate and then process it is orthogonal to that point. E On Tue, Aug 18, 2015 at 1:16 PM, robert bristow-johnson < r...@audioimagination.com> wrote: > On 8/18/15 3:44 PM, Ethan Duni wrote: > >> >Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, -1, 1, >> -1... >> >> The sampling theorem requires that all frequencies be *below* the Nyquist >> frequency. Sampling signals at exactly the Nyquist frequency is an edge >> case that sort-of works in some limited special cases, but there is no >> expectation that digital processing of such a signal is going to work >> properly in general. >> >> But even given that, the interpolator outputting the zero signal in that >> case is exactly correct. That's what you would have gotten if you'd sampled >> the same sine wave (*not* square wave - that would imply frequencies above >> Nyquist) with a half-sample offset from the 1, -1, 1, -1, ... case. The >> incorrect behavior arises when you try to go in the other direction (i.e., >> apply a second half-sample delay), and you still get only DC. >> >> But, again, that doesn't really say anything about interpolation. It just >> says that you sampled the signal improperly in the first place, and so >> digital processing can't be relied upon to work appropriately. >> >> > as suprizing as it may first appear, i think Peter S and me are totally on > the same page here. > > regarding *linear* interpolation, *if* you use linear interpolation in a > precision delay (an LTI thingie, or at least quasi-time-invariant) and you > delay by some integer + 1/2 sample, the filter you get has coefficients and > transfer function > > H(z) = (1/2)*(1 + z^-1)*z^-N > > (where N is the integer part of the delay). > > the gain of that filter, as you approach Nyquist, approaches -inf dB. > > *my* point is that as the delay slowly slides from a integer number of > samples, where the transfer function is > > H(z) = z^-N > > to the integer + 1/2 sample (with gain above), this linear but > time-variant system is going to sound like there is a LPF getting segued in. > > this, for me, is enough to decide never to use solely linear interpolation > for a modulateable delay widget. if i vary delay, i want only the delay to > change. and i would prefer if the delay was the same for all frequencies, > which makes the APF fractional delay thingie problematic. > > bestest, > > r b-j > > >> On Tue, Aug 18, 2015 at 1:40 AM, Peter S <peter.schoffhau...@gmail.com >> <mailto:peter.schoffhau...@gmail.com>> wrote: >> >> On 18/08/2015, Nigel Redmon <earle...@earlevel.com >> <mailto:earle...@earlevel.com>> wrote: >> >> >> >> well, if it's linear interpolation and your fractional delay >> slowly sweeps >> >> from 0 to 1/2 sample, i think you may very well hear a LPF start >> to kick >> >> in. something like -7.8 dB at Nyquist. no, that's not right. >> it's -inf >> >> dB at Nyquist. pretty serious LPF to just slide into. >> > >> > Right the first time, -7.8 dB at the Nyquist frequency, -inf at >> the sampling >> > frequency. No? >> >> -Inf at Nyquist when you're halfway between two samples. >> >> Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, >> -1, 1, -1... >> After interpolating with fraction=0.5, it becomes a constant signal >> 0,0,0,0,0,0,0... >> (because (-1+1)/2 = 0) >> >> > -- > > r b-j r...@audioimagination.com > > "Imagination is more important than knowledge." > > > > > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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