Nowhere was it mentioned that there was an across the frame multiplication with a scalar as far as manipulating the transform coefficients. That might make it time variant. My concept was in the domain of audio engineering which reads a side-chain signal to obtain attenuation factors in the context of EQ. Please see the Wavesfactory Trackspacer to get a sense of what I mean.
On Sun, Mar 8, 2020, 11:02 PM Spencer Russell <s...@media.mit.edu> wrote: > On Sun, Mar 8, 2020, at 7:41 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. > > > But you can avoid this by zero-padding before you do the FFT. In effect > this turns circular convolution into linear convolution - the "tail" ends > up in the zero-pading rather than wrapping around and causing > time-aliasing. This is what overlap-add FFT convolution does. > > In fact, the the standard STFT analysis/synthesis pipeline is the same > thing as overlap-add "fast convolution" if you: > > 1. Use a rectangular window with a length equal to your hop size > 2. zero-pad each input frame by the length of your FIR kernel minus 1 > > Then the regular overlap-add STFT resynthesis is the same as "fast > convolution", and will give you the same thing (to numerical precision) you > would get with a time-domain FIR implementation. > > On Mar 8, 2020, at 2:04 PM, zhiguang zhang <zhiguangezh...@gmail.com> > wrote: > > but bringing up traditional FIR/IIR filtering terminology to describe FFT > filtering doesn't make sense in my mind. I'm not in the audio field. but > yes, I do believe that the system is time invariant, but I don't have time > to prove myself to you on this forum at this time, nor do I have any > interest in meeting Dr Bosi at AES. > > > I don't really understand this perspective - there's a tremendous amount > of conceptual overlap between these ideas, and regimes where they are > completely equivalent (e.g. implementing a time-invariant FIR filter in the > frequency domain using block-by-block "fast convolution"). Certainly when > you're doing time-variant filtering things are somewhat different (e.g. > multiplying in the STFT domain with changing coefficients is doing some > kind of frame-by-frame cross-fading, which will not give the same result as > varying the parameters of an FIR filter on a sample-by-sample basis, in a > pure time-domain implementation). That said, using the same terminology > where we can helps highlight the places where these concepts are related. > > -s > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp
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