" The term Zmw(m-n)of (4.4)isseen to be the sum of the window shifted by m samples. By recognizing that the ex- pression&,w(m-n)issimplyasumofthevaluesofalow- passwindow,itcanbeshown[8]thatifw(n)issampledata sufficiently dense rate, then
w(m-n)= w(ejo) (4.5) m independentofthewindowoffsetn,whereW(ejo)isthevalue of W(e'"), the transform of the window,evaluated at zero frequency. Thus(4.4)becomes Signal xm(ejwS ejwP] showing that the synthesis rule of (4.2) will lead to exact re- construction of x ( n ) boyverlap-adding sections of the waveform. The entire synthesis procedure depends on the sampling re- lation of (4.5). This relationshipisvalid to withinan aliasing error which can be made negligiably smd for sufficiently high sampling rates of the window-i.e., as the sampling rate of the short-time Fourier transform estimates increases, the aliasing error decreases monotonically to zero." so theoretically there is an error that decreases to zero if you sample and window the signal at a sufficiently high rate. this means that, at a practical rate, the error will present itself On Wed, Jun 24, 2020 at 10:49 AM Corey K <corey...@gmail.com> wrote: > Ok, if Allen can't convince you, how about Julius Smith: > https://ccrma.stanford.edu/~jos/sasp/FFT_Filter_Banks.html > <https://urldefense.proofpoint.com/v2/url?u=https-3A__ccrma.stanford.edu_-7Ejos_sasp_FFT-5FFilter-5FBanks.html&d=DwMFaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=plfrvjCcmcM2a19j0pocTY0nlPoVxogY9T9_uOAxrAQ&s=5g05rZmCxxm7mFWzjsmtibiAFhpNr6ZMNi72oy2iEf0&e=> > ? > > > > On Wed, Jun 24, 2020 at 12:13 PM Zhiguang Eric Zhang <zez...@nyu.edu> > wrote: > >> Thank you. Yes it seems very theoretical and math heavy. In practice >> you will get this frequency response artifact no matter how small. It >> should factor into the math in some way, perhaps they are not looking at >> the laplacian >> >> On Wed, Jun 24, 2020, 10:41 AM Corey K <corey...@gmail.com> wrote: >> >>> It's a classic paper. Google scholar shows it has been cited over 1000 >>> times. There's a link to it here here: >>> https://jontalle.web.engr.illinois.edu/uploads/537/Papers/Public/AllenRabiner77-ProcIEEE.pdf >>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__jontalle.web.engr.illinois.edu_uploads_537_Papers_Public_AllenRabiner77-2DProcIEEE.pdf&d=DwMFaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=EIWxvlh8qpdcU_coPNdiZxhQaqJEihTl-BcA8WN1eWw&s=e-NKtVrjHEINB5kEwTE3d4g9q2bZGxjnso8yyBhaUUM&e=> >>> >>> >>> On Wed, Jun 24, 2020 at 11:56 AM Zhiguang Eric Zhang <zez...@nyu.edu> >>> wrote: >>> >>>> unfortunately, i'm not familiar with that paper. could you please >>>> attach it or provide a link for reference? the Gibbs phenomenon is >>>> actually a very well-known and thoroughly characterized signal processing >>>> artifact that has been approached from a variety of angles as far as trying >>>> to find a solution. iit can be thought of as an unavoidable digital filter >>>> response of having to take X number of samples in one snapshot while >>>> capturing a finite instance in time (as you might know the Dirac delta is >>>> centered on DC) >>>> >>>> https://en.wikipedia.org/wiki/Ringing_artifacts >>>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__en.wikipedia.org_wiki_Ringing-5Fartifacts&d=DwMFaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=w_CiiFx8eb9uUtrPcg7_DA&m=EIWxvlh8qpdcU_coPNdiZxhQaqJEihTl-BcA8WN1eWw&s=XkZObRCqtj2hzKnIyyVYQqrxJYhSfTrXnDzaDFzTsw4&e=> >>>> >>>> On Wed, Jun 24, 2020 at 10:12 AM Corey K <corey...@gmail.com> wrote: >>>> >>>>> I think you're mistaken, unfortunately. Block FFT convolution has been >>>>> around for 30+ years. In 1977 (43 years ago now), Jont Allen showed in his >>>>> paper "A Unified Approach to Short-Time Fourier Analysis" how you can >>>>> perform FIR filtering perfectly with the FFT, of COLA windows are used. >>>>> See >>>>> equation 5.2.5 in that paper, and the analysis that precedes it. >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> On Wed, Jun 24, 2020 at 11:16 AM Zhiguang Eric Zhang <zez...@nyu.edu> >>>>> wrote: >>>>> >>>>>> 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= >>>>>> >>>>>> _______________________________________________ >>>>>> 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=cdkdusrQSRQeoIdvFPBw-IHlrTvjeJt4YV8Nkf2Zfd4&s=WaORGHf6gkBiBL4HM9z9I3P-lBjNVIi5TkMPBpzVmfY&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=cdkdusrQSRQeoIdvFPBw-IHlrTvjeJt4YV8Nkf2Zfd4&s=WaORGHf6gkBiBL4HM9z9I3P-lBjNVIi5TkMPBpzVmfY&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=EIWxvlh8qpdcU_coPNdiZxhQaqJEihTl-BcA8WN1eWw&s=mT1huoxSaty-HqNoCoJq46lZ1fhEmudUf99Jcq71FRw&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=EIWxvlh8qpdcU_coPNdiZxhQaqJEihTl-BcA8WN1eWw&s=mT1huoxSaty-HqNoCoJq46lZ1fhEmudUf99Jcq71FRw&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=plfrvjCcmcM2a19j0pocTY0nlPoVxogY9T9_uOAxrAQ&s=nYILQ8M3mB1pn1HCMmkHnW6ysx7p-NYsoz7pPMwcyZ0&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=plfrvjCcmcM2a19j0pocTY0nlPoVxogY9T9_uOAxrAQ&s=nYILQ8M3mB1pn1HCMmkHnW6ysx7p-NYsoz7pPMwcyZ0&e=
_______________________________________________ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
