On 21/08/2015, Ethan Duni <ethan.d...@gmail.com> wrote: >>It shows *exactly* the aliasing.... > > It shows the aliasing left by linear interpolation into the continuous time > domain. It doesn't show the additional aliasing produced by then delaying > and sampling that signal. I.e., the images that would get folded back onto > the new baseband, disturbing the sinc^2 curve.
This image doesn't involve any fractional delay. > Those differences would be quite small for resampling to 44.1kHz with no > delay, since the oversampling ratio is considerable, so you'd have to look > carefully to see them. I think they're actually on the image: http://morpheus.spectralhead.com/img/resampling_aliasing.png They're hard to notice, because the other aliasing masks it. > This is a big hint that they are not portrayed: > Ollie knows what he is doing, so if he wanted to illustrate the effects of > the resampling, he would have constructed a scenario where they are easily > visible. Since that image is not meant to "illustrate the effects of resampling", but rather, to "illustrate the effects of interpolation", *obviously* it doesn't focus on the aliasing from the resampling. Therefore, it is not a "hint" at all, and your argument is invalid. > And probably mentioned a second sample rate, explicitly shown both > the sinc^2 and its aliased counterpart, etc. The effect would be shown in a > visible, explicit manner, if that was what the graph was supposed to show. The fact that this graph is not supposed to demonstrate the aliasing from the resampling, does not mean that 1) it's not there on the graph (it's just barely visible) 2) the images of the continuous time interpolated signal are not aliasing. That's also called aliasing!!! > But all of those things depend on parameters like oversampling ratio and > delay, so it would be a much more complicated picture. Yes, and that's all entirely irrelevant here... Because the images in the continuous time signal before the resampling are also called aliasing!!! They're all aliases of the original spectrum, and they all alias back to the original spectrum when sampled at the original sampling rate! They're called aliasing even before you resample them! > What we're shown > here is just the effects of polynomial interpolation to get to the > continuous time domain. False. I've shown the FFT frequency spectra of actual upsampled signals. > The additional effects of delaying and then > sampling that signal back into the discrete time domain are not visible. There was no delaying involved at all. The effects of "sampling that signal back" are not visible, because there's 88x oversampling, just as I pointed out. If you want, you can repeat the same with less oversampling, and present us your results. > It seems that you have assumed that some resampling must be happening > because the graph only goes up to 22kHz. But that's just the range of the > graph, you don't need to do any resampling of anything to graph sinc^2 over > any particular range of frequencies. I never said you need do to resampling of the continuous time signal to graph sinc^2. I said: the images in the frequency spectrum of the continuous time signal are aliases of the original spectrum, and they alias back to the original spectrum when the continuous time signal is sampled at the original rate! > But that's not quite the exact same graph. It's essentially the exact same graph. > And why are you putting a sound card in the loop? That was the most convenient way to record the signal. > This is all just digital processing in question here. You > don't even need to process any signals, there are analytic expressions for > all of the quantities involved. That's just one way of drawing fancy graphs. FFT is another way of drawing fancy graphs. Why would I restrict myself to one method? > That's how Ollie generated graphs of them > without reference to any particular signals. How do you know? Prove it! I'm convinced he generated it via numerical means and FFT. > Again, the differences in question are small due to the high oversampling > ratio, so it's going to be quite difficult to see them in macroscopic > graphs like this. Let me point out again, that all those spectral images in the continunous time signal before the resampling, *are* aliasing, as they're aliases of the original spectrum, and are *very* visible on the graph! > If you want to see the differences, just make a plot of > both sinc^2 and its aliased versions (for whatever oversampling ratios > and/or delays), and look at the differences. It won't be interesting for > high oversampling ratios and zero delay - which is exactly why that > scenario is a poor choice for illustrating the effects in question. And you're entirely missing the point what it is supposed to illustrate. > The fact that sampling a continuous time signal at a very high rate results > in a spectrum that closely resembles the continuous time spectrum (over the > sampled bandwidth) is beside the point. Exactly. It's totally beside the point, and has nothing to do with the question. > It just means that you're operating > in a regime where the effects are very hard to spot. If you cannot see the aliased peaks on the interpolated sine wave's FFT graph, that can only mean that you're blind. They're *very* visible. > It doesn't follow from > that resemblance that resampling must be occurring to get a plot of the > spectrum of the continuous time signal. And no one claimed that. -P _______________________________________________ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
