>Nope. Ever heard of multistage interpolation? I'm well aware that multistage interpolation gives cost savings relative to single-stage interpolation, generally. That is beside the point: the costs of interpolation all still scale with oversampling ratio and quality requirements, just like in single stage interpolation. There's no magic to multi-stage interpolation that avoids that relationship.
>that's just plain wrong and stupid, and that's what all advanced multirate books >will also tell you. You've been told repeatedly that this kind of abusive, condescending behavior is not welcome here, and you need to cut it out immediately. >Tell me, you don't have an extra half kilobyte of memory in a typical >computer? There are lots of dsp applications that don't run on personal computers, but rather on very lightweight embedded targets. Memory tends to be at a premium on those platforms. E On Wed, Aug 19, 2015 at 3:55 PM, Peter S <peter.schoffhau...@gmail.com> wrote: > On 20/08/2015, Ethan Duni <ethan.d...@gmail.com> wrote: > > > > I don't dispute that linear fractional interpolation is the right choice > if > > you're going to oversample by a large ratio. The question is what is the > > right balance overall, when considering the combined costs of > > the oversampler and the fractional interpolator. > > It's hard to tell in general. It depends on various factors, including: > > - your desired/available CPU usage > - your desired/available memory usage and cache size > - the available instruction set of your CPU > - your desired antialias filter steepness > - your desired stopband attenuation > > ...and possibly other factors. Since these may vary largely, I think > it is impossible to tell in general. What I read in multirate > literature, and what is also my own experience, is that - when using a > relatively large oversampling ratio - then it's more cost-effective to > use linear interpolation at the higher stages (and that's Olli's > conclusion as well). > > > You can leverage any finite interpolator to skip computations in an FIR > > oversampler, not just linear. You get the most "skipping" in the case of > > high oversampling ratio and linear interpolation, but the same trick > still > > works any time your oversampling ratio is greater than your interpolator > > order. > > But to a varying degree. A FIR interpolator is still "heavy" if you > skip samples where the coefficient is zero, compared to linear > interpolation (but it is also higher quality). > > > The flipside is that the higher the oversampling ratio, the longer the > FIR > > oversampling filter needs to be in the first place. > > Nope. Ever heard of multistage interpolation? You may do a small FIR > stage (say, 2x or 4x), and then a linear stage (or another, > low-complexity FIR stage according to your desired specifications, or > even further stages). Seems you still don't understand that you can > oversample in multiple stages, and use a linear interpolator for the > higher stages of oversampling... Which is almost always optimal than > using a single costy FIR filter to do the interpolation. You don't > need to use a 512x FIR at >100 dB stopband attentuation, that's just > plain wrong and stupid, and that's what all advanced multirate books > will also tell you. > > Same for IIR case. > > >>Since memory is usually not an issue, > > > > There are lots of dsp applications where memory is very much the main > > constraint. > > Tell me, you don't have an extra half kilobyte of memory in a typical > computer? I hear, those have 8-32 GB of RAM nowadays, and CPU cache > sizes are like 32-128 KiB. > > > The performance of your oversampler will be garbage if you do that. And > so > > there will be no point in worrying about the quality of fractional > > interpolation after that point, since the signal you'll be interpolating > > will be full of aliasing to begin with. > > Exactly. But it won't be "heavy"! So it's not the "oversampling" what > makes the process heavy, but rather, the interpolation / anti-aliasing > filter!! > > > And that means it needs lots of resources, especially as the oversampling > > ratio gets large. It's the required quality that drives the oversampler > > costs (and filter design choices). > > Which is exactly what I said. If your specification is low, you can > have a 128x oversampler that is (relatively) "low-cost". It's not the > oversampling ratio what matters most..... > > > If you are willing to accept low quality in order to save on CPU (or > maybe > > there's nothing in the upper frequencies that you're worried about), then > > there's no point in resampling at all. Just use a low order fractional > > interpolator directly on the signal. > > Seems you still miss the whole point of multistage interpolation. I > recommend you read some books / papers on multirate processing. > > >>It should also be noted that the linear interpolation can be used for > >>the upsampling itself as well, reducing the cost of your oversampling, > > > > Again, that would add up to a very low quality upsampler. > > You're wrong. Read Olli Niemitalo's paper again (and some multirate > books). When the oversampling ratio is high and the signal is already > oversampled, linear interpolation is (nearly) optimal. That implies a > multistage upsampler, which is typically computationally a lot more > optimal than a single-stage one. Just as the multirate signal > processing literature will tell you in detail. > > -P > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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