Re: [music-dsp] Sliding Phase Vocoder (was FIR blog post & interactive demo)
On Wed, Jun 24, 2020 at 8:56 PM Zhiguang Zhang wrote: > the Gibbs "nastiness' is ever present in both hardware and software > implementations. It's just there in the underlying physics of sampling > theory, even in the analog domain it seems :) It's not really related to sampling. A bandlimited analog continuous time signal has 'ringing'-- it's part of the definition of being band limited. Sometimes in the sampled context the ringing is hidden between the samples, but will show up in the analog reconstruction or after correct digital processing that applies a fractional sample phase shift. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Sliding Phase Vocoder (was FIR blog post & interactive demo)
On Wed, Jun 24, 2020 at 7:46 PM Russell Wedelich wrote: > Respectively Eric, I think you may be confusing two different use cases > for windows. Your recent reference is referring to constructing FIR filters > via the Windowing method of ideal brickwall filters. This is different from > a frequency domain convolution implementation of an FIR filter (which may > or may not explicitly apply a smooth window) which as far as I can tell is > the origin of this part of the discussion. > And for the convolution implementation of a FIR filter if you were to compare _correct_ implementations of each approach which had adequate(*) internal precision relative to the output, the results would be _bit identical_. (*) In practice, digital implementations of *both* time domain FIR and convolution typically lack enough internal precision such that their output is exact, and as a result they won't be bit identical. Though I wouldn't be surprised if, for a given internal precision, a WOLA implementation using FFTs wasn't *more* faithful to a infinite precision FIR than the same FIR implemented with limited precision, due to the smaller circuit depth for the frequency domain approach. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] FIR blog post & interactive demo
On Sun, Mar 8, 2020 at 11:41 PM Ethan Duni wrote: > FFT filterbanks are time variant due to framing effects and the circular > convolution property. They exhibit “perfect reconstruction” if you design the > windows correctly, but this only applies if the FFT coefficients are not > altered between analysis and synthesis. If you alter the FFT coefficients > (i.e., “filtering”), it causes time domain aliasing. If the system is suitably designed (e.g. correct window and overlap), you can filter using an FFT and get identical results to a time domain FIR filter (up-to rounding/precision limits, of course). The appropriate window and overlap process will cause all circular convolution artefacts to cancel. In fact, one particularly computationally efficient method to apply a very long FIR filter (e.g. for reverbs) with low delay is to factor it into a low delay portion and one or more longer delay chunks and use naive convolution for the low delay portion and large overlapped FFTs for the high delay portions. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
