The details of how the graphs were generated don't really matter. The point is that the only effect shown is the spectrum of the continuous-time polynomial interpolator. The additional spectral effects of delaying and resampling that continuous-time signal (to get fractional delay, for example) are not shown. There is no "resampling" to be seen in the graphs.
>I claim that they are aliases of the original spectrum. What we see in the graph is simply the spectra of the continuous-time interpolators. Since the spectra extend beyond the original nyquist rate, there will indeed be images of the original signal weighted by the interpolator spectrum present in the continuous-time interpolated signal. Whether those are ultimately expressed as aliases depends on what you then do with that continuous time signal. If you resample to the original rate (in order to implement a fractional delay, say), then those weighted images will be folded back to the same place they came from. In that case, there is no aliasing, you just end up with a modified frequency response of your fractional interpolator. This is where the zero at Nyquist comes from when we do a half-sample delay - the linear phase term corresponding to a half-sample delay causes the signal images to become out of phase with each other as you approach Nyquist, so they cancel out and you get a zero. It is only if the interpolated continuous-time signal is resampled at a different rate, or just used directly, that those signal images end up expressed as aliases. The rest of your accusations are your usual misreadings and straw men. I won't be legitimating them by responding, and I hope you will accept that and give up on these childish tactics. It would be better for everyone if you could make a point of engaging in good faith and trying to stick to the subject rather than attacking the intellects of others. E On Fri, Aug 21, 2015 at 2:05 PM, Peter S <peter.schoffhau...@gmail.com> wrote: > Also, you even contradict yourself. You claim that: > > 1) Olli's graph was created by graphing sinc(x), sinc^2(x), and not via > FFT. > > 2) The artifacts from the resampling would be barely visible, because > the oversampling rate is quite high. > > So, if - according to 2) - the artifacts are not visible because the > oversampling is high and the graph doesn't focus on that, then how do > you know that 1) is true? You claim that the resampling artifacts > wouldn't be visible anyways. > > If that's true, then how would you prove that FFT was not used for > creating Olli's graph? > > Also, even you yourself acknowledge that > > "It shows the aliasing left by linear interpolation into the > continuous time domain." > > So, we agree that the graph shows aliasing, right? > > I do not know where you get your idea of "additional aliasing" - it's > the very same aliasing, except the resampling folds it back... > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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