Not totally understanding you, unfortunately. But if what you are describing is part of the normal filter response/ringing I guess I wouldn't refer to it as "artifacts"? FIR filtering can be performed equivalently in the time or frequency domain. Do you disagree with that statement?
On Wed, Jun 24, 2020 at 10:02 AM Zhiguang Eric Zhang <zez...@nyu.edu> wrote: > yes but any windowing operation is akin to taking a dirac delta function > on X number of samples and thus you will get ringing/ripple artifacts as a > necessary part of the filter response > > On Wed, Jun 24, 2020 at 6:30 AM Corey K <corey...@gmail.com> wrote: > >> >> of course it won't have the ripple artifacts associated with FFT overlap >>> windowing >>> >> >> What is the ripple artifact you are talking about? When using constant >> overlap add (COLA) windows the STFT is a perfect reconstruction filterbank. >> Likewise block FFT convolution can be used to implement any FIR filtering >> operation. >> >> >> >> >> >> >>> cheers, >>> -ez >>> >>> On Mon, Apr 13, 2020 at 4:55 PM Andreas Gustafsson <g...@waxingwave.com> >>> wrote: >>> >>>> Hello Spencer, >>>> >>>> You wrote: >>>> > A while ago I read through some the literature [1] on implementing >>>> > an invertible CQT as a special case of the Nonstationary Gabor >>>> > Transform. It's implemented by the essentia library [2] among other >>>> > places probably. >>>> > >>>> > The main idea is that you take the FFT of your whole signal, then >>>> > apply the filter bank in the frequency domain (just >>>> > multiplication). Then you IFFT each filtered signal, which gives you >>>> > the time-domain samples for each band of the filter bank. Each >>>> > frequency-domain filter has a different bandwidth, so your IFFT is a >>>> > different length for each one, which gives you the different sample >>>> > rates for each one. >>>> >>>> That's the basic idea, but the Gaborator rounds up each of the >>>> per-band sample rates to the original sample rate divided by some >>>> power of two. This means all the FFT sizes can be powers of two, >>>> which tend to be faster than arbitrary sizes. It also results in a >>>> nicely regular time-frequency sampling grid where many of the samples >>>> coincide in time, as shown in the second plot on this page: >>>> >>>> >>>> https://urldefense.proofpoint.com/v2/url?u=https-3A__www.gaborator.com_gaborator-2D1.4_doc_overview.html&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=4rIFY1X4fS1G8-882xM72jF9DvsY6-Z2ckeHxjPPfTY&s=FG-ZGfFa09T-Y7nLajB8evbCy9WIADFrUqPwjz-LHow&e= >>>> >>>> Also, the Gaborator makes use of multirate processing where the signal >>>> is repeatedly decimated by 2 and the calculations for the lower >>>> octaves run at successively lower sample rates. These optimizations >>>> help the Gaborator achieve a performance of millions of samples per >>>> second per CPU core. >>>> >>>> > They also give an "online" version where you do >>>> > the processing in chunks, but really for this to work I think you'd >>>> > need large-ish chunks so the latency would be pretty bad. >>>> >>>> The Gaborator also works in chunks. A typical chunk size might be >>>> 8192 samples, but thanks to the multirate processing, in the lowest >>>> frequency bands, each of those 8192 samples may represent the >>>> low-frequency content of something like 1024 samples of the original >>>> signal. This gives an effective chunk size of some 8 million samples >>>> without actually having to perform any FFTs that large. >>>> >>>> Latency is certainly high, but I would not say it is a consequence of >>>> the chunk size as such. Rather, both the high latency and the need >>>> for a large (effective) chunk size are consequences of the lengths of >>>> the band filter impulse responses, which get exponentially larger as >>>> the constant-Q bands get narrower towards lower frequencies. >>>> >>>> Latency in the Gaborator is discussed in more detail here: >>>> >>>> >>>> https://urldefense.proofpoint.com/v2/url?u=https-3A__www.gaborator.com_gaborator-2D1.4_doc_realtime.html&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=4rIFY1X4fS1G8-882xM72jF9DvsY6-Z2ckeHxjPPfTY&s=uuRzi0taGcXI9Sq63G_xTTrCjaz9cu3ewu8jfzIUcVc&e= >>>> >>>> > The whole process is in some ways dual to the usual STFT process, >>>> > where we first window and then FFT. in the NSGT you first FFT and >>>> > then window, and then IFFT each band to get a Time-Frequency >>>> > representation. >>>> >>>> Yes. >>>> >>>> > For resynthesis you end up with a similar window overlap constraint >>>> > as in STFT, except now the windows are in the frequency domain. It's >>>> > a little more complicated because the window centers aren't >>>> > evenly-spaced, so creating COLA windows is complicated. There are >>>> > some fancier approaches to designing a set of synthesis windows that >>>> > are complementary (inverse) of the analysis windows, which is what >>>> > the frame-theory folks like that Austrian group seem to like to use. >>>> >>>> The Gaborator was inspired by the papers from that Austrian group and >>>> uses complementary resynthesis windows, or "duals" as frame theorists >>>> like to call them. The analysis windows are Gaussian, and the dual >>>> windows used for resynthesis end up being slightly distorted >>>> Gaussians. >>>> >>>> > One of the nice things about the NSGT is it lets you be really >>>> > flexible in your filterbank design while still giving you >>>> > invertibility. >>>> >>>> Agreed. >>>> >>>> In a later message, you wrote: >>>> > Whoops, just clicked through to the documentation and it looks like >>>> > this is the track you're on also. I'm curious if you have any >>>> > insight into the window-selection for the analysis and synthesis >>>> > process. It seems like the NSGT framework forces you to be a bit >>>> > smarter with windows than just sticking to COLA, but the dual frame >>>> > techniques should apply for regular STFT processing, right? >>>> >>>> I'm actually not that familiar with traditional STFTs and COLA, but as >>>> far as I can tell, the STFT is a special case of the NSGT and the same >>>> dual frame techniques should apply. >>>> -- >>>> Andreas Gustafsson, g...@waxingwave.com >>>> _______________________________________________ >>>> dupswapdrop: music-dsp mailing list >>>> music-dsp@music.columbia.edu >>>> >>>> https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.columbia.edu_mailman_listinfo_music-2Ddsp&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=4rIFY1X4fS1G8-882xM72jF9DvsY6-Z2ckeHxjPPfTY&s=br6gIADk3PB9_kF8YoA7aZdcf5McFvCCOlyYso5D2BI&e= >>>> >>> _______________________________________________ >>> dupswapdrop: music-dsp mailing list >>> music-dsp@music.columbia.edu >>> https://lists.columbia.edu/mailman/listinfo/music-dsp >>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.columbia.edu_mailman_listinfo_music-2Ddsp&d=DwMFaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=0Zfr9NX2z_qbqorZ4mvWlKWdhvCOnws4tZKFE3J0lxI&s=_0-DUAEnNzJ0nyrUgGHozY0ob4n_-0OWpipEf-p2Bps&e=> >> >> _______________________________________________ >> dupswapdrop: music-dsp mailing list >> music-dsp@music.columbia.edu >> >> https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.columbia.edu_mailman_listinfo_music-2Ddsp&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=0Zfr9NX2z_qbqorZ4mvWlKWdhvCOnws4tZKFE3J0lxI&s=_0-DUAEnNzJ0nyrUgGHozY0ob4n_-0OWpipEf-p2Bps&e= > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp
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