> On March 20, 2020 2:45 PM STEFFAN DIEDRICHSEN <sdiedrich...@me.com> wrote: > > > Actually, you can do a window size per bin and an arbitrary spacing of the > frequencies and create a “true” constant Q SDFT. Somehow, it reminds me on > the modal synthesis stuff, which can be used to create weird processing. >
yeah. there would be no Cooley-Tukey goin' on here. essentially, it's a bank of resonant filters. perhaps one could come up with complementary spectral envelopes in the log(f) scale that would add to 1. but i dunno if you could get such a sliding window using truncated IIR filters, so the Fourier Transform of it looks like one of these complementary spectral envelopes. if it doesn't, adding the results of these will not get you perfect reconstruction. > Regarding Corona: I’m doing home office with a view on my garden. Vermont is > not the worst place to holed in, right? How is the supply with TP? before the crisis onset, we had two 12-roll packages, one hasn't been opened. i'm not too uncomfortable about provisions. i haven't yet seen the store yet, but i might this afternoon (that'll be sobering). i need to buy some booze. i live at the mouth of a river into Lake Champlain (44.527966 lat, -73.270829 long). it's 2-dimensional, but i have a 200 acre natural waterpark in my back yard. with the snow cover in the watershed melting, i'll be canoeing in maybe 24 hours or less (and remain within the city limits of the most populous city in the state.) but i am pretty concerned about the present thing and i was around for cold war, Cuban missile crisis, JFK assassination, 1968 (two assassinations, burning streets, Chicago DNC), U.S. president forced out of office mid-term, 911 and this is worrisome. i should have converted my TIAA-CREF retirement investment from stock to bonds last January. There's not that much in there, but it looks like the curves of the markets. > > Steffan > > PS.: Did somebody not see the formulas in my post? They were embedded pdfs > made in Grapher. > i edited it out. anyway, while i have done this sliding Hann window before, i haven't done it for a sliding DFT. but i would be excited to see a good implementation of constant Q filterbank that is very close to perfect reconstruction if the modification in the frequency domain is null. one could make a Hann windowed DTFT evaluated at a finite number of arbitrary frequencies. i just wonder if a sliding Hann window would be best. but, using a truncated cosine as the impulse response of the TIIR, whatever shape of the window would have to be a sum of truncated cosines (plus the constant term). but you could make a nice frequency analyzer of log-spaced, constant-Q, filterbanks with a bank of truncated IIRs and pre-multiplying the input to each filter by e^(-j omega n). making them add up to a wire is a harder problem. -- r b-j r...@audioimagination.com "Imagination is more important than knowledge." _______________________________________________ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
