that's not true. with FFT/COLA you will necessarily have the Gibbs phenomenon / ringing / ripple artifacts. certain window types will minimize this but you will get this phenomenon nonetheless.
On Wed, Jun 24, 2020 at 9:44 AM Corey K <corey...@gmail.com> wrote: > I see what you're getting at, I suppose. However, in the context of FIR > filtering I wouldn't refer to this as an artifact. Let's say you gave me an > FIR filter with N-taps and asked me to write a program to implement that > filter. I could implement this using a direct form structure (in the > time-domain), or with the FFT using OLA. Both would give the exact same > results down to numerical precision, with no "artifacts". That's why it > intrigued me when you said "of course it won't have the ripple artifacts > associated with FFT overlap windowing" when referring to software that does > filtering. > > > On Wed, Jun 24, 2020 at 10:59 AM Zhiguang Eric Zhang <zez...@nyu.edu> > wrote: > >> ripple is just a known artifactual component of a windowing operation. >> it's also known as the Gibbs phenomenon >> >> http://matlab.izmiran.ru/help/toolbox/signal/filterd8.html >> <https://urldefense.proofpoint.com/v2/url?u=http-3A__matlab.izmiran.ru_help_toolbox_signal_filterd8.html&d=DwMFaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=LVW8eOM2POVbM1MauwqppWYiBwmnAs5_i7qiMOEK0-o&s=XefFmTg_gx0qQrZnZTOJDTlaqMl3xt5WBzqxYAkoMKA&e=> >> >> i'm not referring to any equivalency between time/freq domain filtering >> >> >> On Wed, Jun 24, 2020 at 9:21 AM Corey K <corey...@gmail.com> wrote: >> >>> 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 >>>> <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=ggIGGD37NXAIrRak00WIRysmpvCxdGGCHkoma2TGgxc&s=2aCxaadCSRm8GtUxELE7DhnWmqkKUkkAymUl19tD-v4&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=ggIGGD37NXAIrRak00WIRysmpvCxdGGCHkoma2TGgxc&s=2aCxaadCSRm8GtUxELE7DhnWmqkKUkkAymUl19tD-v4&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=LVW8eOM2POVbM1MauwqppWYiBwmnAs5_i7qiMOEK0-o&s=Wiyf_pAPkjR4_Ox3pi0vTvCNZDjINUsf0bfxVKpiGW8&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=LVW8eOM2POVbM1MauwqppWYiBwmnAs5_i7qiMOEK0-o&s=Wiyf_pAPkjR4_Ox3pi0vTvCNZDjINUsf0bfxVKpiGW8&e=
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