>If all you're trying to do is mitigate the rolloff of linear interp That's one concern, and by itself it implies that you need to oversample by at least some margin to avoid having a zero at the top of your audio band (along with a transition band below that).
But the larger concern is the overall accuracy of the interpolator. At low oversampling ratios, the sinc^2 rolloff of the linear interpolator response isn't effective at squashing the signal images, so you end up with aliasing corrupting your results. Hence the need for higher order interpolation at lower oversampling ratios, as described in Ollie's paper. If you want to get high SNR out of linear interpolation, you need to crank up the oversampling considerably - far beyond what is needed just to avoid the attenuation of high frequencies of the in-band component, in order to sufficiently squash the images. E On Thu, Aug 20, 2015 at 12:18 PM, Chris Santoro <chris.sant...@gmail.com> wrote: > As far as the oversampling + linear interpolation approach goes, I have to > ask... why oversample so much (512x)? > > Purely from a rolloff perspective, it seems you can figure out what your > returns are going to be by calculating sinc^2 at (1/upsample_ratio) for a > variety of oversampling ratios. Here's the python code to run the numbers... > > #------------------------------------------------- > import numpy as np > > #normalized frequency points > X = [1.0/512.0, 1.0/256.0, 1.0/128.0, 1.0/64.0, 1.0/32.0, 1.0/16.0, > 1.0/8.0, 1.0/4.0] > #find attenuation at frequency points due to linear interpolation worst > case (halfway in between) > S = np.sinc(X) > S = 20*np.log10(S*S) > > print S > #----------------------------------------------- > > and here's what it spits out for various attenuation values at what would > be nyquist in the baseband: > > 2X: -7.8 dB > 4X: -1.8 dB > 8X: -0.44 dB > 16X: -0.11 dB > 32X: -0.027 dB > 64X: -0.0069 dB > 128X: -0.0017 dB > 256X: -0.00043 dB > 512X: -0.00010 dB > > If all you're trying to do is mitigate the rolloff of linear interp, it > looks like there's diminishing returns beyond 16X or 32X, where you're > talking about a tenth of a dB or less at nyquist, which most people can't > even hear in that range. Your anti-aliasing properties are going to be > determined by your choice of upsampling/windowed-sync/anti-imaging filter > and how long you want to let that be. Or am I missing something? It just > doesn't seem worth it go to that high. > > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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