>1) Olli Niemiatalo's graph *is* equivalent of the spectrum of >upsampled white noise.
We've been over this repeatedly, including in the very post you are responding to. The fact that there are many ways to produce a graph of the interpolation spectrum is not in dispute, nor is it germaine to my point. I'm not sure what you're trying to accomplish by harping on this point, while ignoring everything I say. Certainly, it is not convincing me that you have some worthwhile response to my points, or even that you are understanding them in the first place. It's seems like you are trying to avoid my point entirely, in favor of some imaginary dispute of your own invention, which you think you can "win." >Have you actually looked at Olli Niemitalo's graph closely? >Here is proof that it is NOT a graph of sinc(x)/sinc^2(x): > >http://morpheus.spectralhead.com/img/other001-analysis.gif > >It is NOT sinc(x)/sinc^2(x), and you're blind as a bat if you do not see that. I have no idea what you think you are proving by scrutinizing graph artifacts like that, but it's a preposterous approach to signal analysis on its face. It's also in extremely poor taste to use "retard" as a term of abuse. People with mental disabilities have it hard enough already, without others treating their status as an insult to be thrown around. I'd appreciate it if you would compose yourself and refrain from these kinds of ugly outbursts. Meanwhile, it seems that you are suggesting that the spectrum of white noise linearly interpolated up to a high oversampling rate is not sinc^2. Is your whole point here that generating such a plot by FFTing the interpolation of a finite segment of white noise will produce finite-data artifacts in the resulting graph? Because that's not relevant to the subject, and only goes to show that it's better to just graph the sinc^2 curve directly and so avoid all of the excess computation and finite-data effects. Are you claiming that those wiggles in the graph represent aliasing of the spectrum from resampling at 44.1kHz? If so, that is unlikely. You do agree that the spectrum of a continuous-time linear interpolator is given by sinc^2, right? E On Fri, Aug 21, 2015 at 4:59 PM, Peter S <peter.schoffhau...@gmail.com> wrote: > Since you constantly derail this topic with irrelevant talk, let me > instead prove that > > 1) Olli Niemiatalo's graph *is* equivalent of the spectrum of > upsampled white noise. > 2) Olli Niemitalo's graph does *not* depict sinc(x)/sinc^2(x). > > First I'll prove 1). > > Using palette modification, I extracted the linear interpolation curve > from Olli's figure: > http://morpheus.spectralhead.com/img/other001b.gif > > Then I sampled white noise at 500 Hz, and resampled it to 44.1 kHz > using linear interpolation. I got this spectrum: > > http://morpheus.spectralhead.com/img/resampled_noise_spectrum.gif > > To do a proper A/B comparison between the two spectra, I tried to > align and match them as much as possible, and created an animated GIF > file that blinks between the two graphs at a 500 ms rate: > > http://morpheus.spectralhead.com/img/olli_vs_resampled_noise.gif > > Although the alignment is not 100% exact, to my eyes, they look like > totally equivalent graphs. > > This proves that upsampled white noise has the same spectrum as the > graph shown on Olli's graph for linear interpolation. > > Second, I'll prove 2). > > Have you actually looked at Olli Niemitalo's graph closely? > Here is proof that it is NOT a graph of sinc(x)/sinc^2(x): > > http://morpheus.spectralhead.com/img/other001-analysis.gif > > It is NOT sinc(x)/sinc^2(x), and you're blind as a bat if you do not see > that. > > Since I proved both 1) and 2), it is totally irrelevant what you say, > because none of what you could ever say would disprove this. > > Sinc(x) does not have a jagged/noisy look, therefore it is 100% > certain it is not what you see on Olli's graph. Point proven, end of > discussion. > > -P > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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