On 21/08/2015, Ethan Duni <ethan.d...@gmail.com> wrote: >>Creating a 22000 Hz signal from a 250 Hz signal by interpolation, is >>*exactly* upsampling > > That is not what is shown in that graph. The graph simply shows the > continuous-time frequency response of the interpolation polynomials, > graphed up to 22kHz. No resampling is depicted, or the frequency responses > would show the aliasing associated with that.
It shows *exactly* the aliasing.... http://morpheus.spectralhead.com/img/interpolation_aliasing.png There are about 88 alias images visible on the graph. The linear interpolation curve is not "smooth", so it contains aliasing. > It's just showing the sinc^2 > response of the linear interpolator, and similar for the other polynomials. If the signal you interpolate is white noise, and the spectrum of the signal is a flat spectrum rectangle like the one displayed, then after resampling, you get *exactly* the spectrum you see on the graph, showing 88 alias images. Proof: I created 60 seconds of white noise sampled at 500 Hz, then resampled it to 44.1 kHz using linear interpolation. After the upsampling, it sounds like this: http://morpheus.spectralhead.com/wav/noise_resampled.wav Its spectrum looks like this: http://morpheus.spectralhead.com/img/noise_resampled.png Looks familiar? Oh, it's the *exact* same graph! (Minus some difference above 20 kHz, due to my soundcard's anti-alias filter.) It is an FFT graph of the upsampled white noise, and it shows *exactly* the aliasing. Good morning! > This is what you'd get if you used those interpolation polynomials to > convert a 250Hz sampled signal into a continuous time signal, not a > discrete time signal of whatever sampling rate. Nope. You get the same graph if you sample that continuous time signal at a 44.1 kHz sampling rate (with some further aliasing from the sampling). Just as I've shown. Besides, I think the graph was created via numerical means using FFT, because it has noise at the low ampliutes (marked on the image). Therefore, it doesn't show a continuous time sinc^2 graph, because that wouldn't be noisy. -P _______________________________________________ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
