I don't think that's correct -- DIF involves first doing a single stage of butterfly operations over the input, and then doing two smaller DFTs on that preprocessed data. I don't think there is any reasonable way to take two "consecutive" DFTs of the raw input data and combine them into a longer DFT.
(And I don't know anything about the historical question!) -Ethan On Mon, Nov 5, 2018 at 2:18 PM, robert bristow-johnson < r...@audioimagination.com> wrote: > > > Ethan, that's just the difference between Decimation-in-Frequency FFT and > Decimation-in-Time FFT. > > i guess i am not entirely certainly of the history, but i credited both > the DIT and DIF FFT to Cooley and Tukey. that might be an incorrect > historical impression. > > > > ---------------------------- Original Message ---------------------------- > Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for > realtime synthesis? > From: "Ethan Fenn" <et...@polyspectral.com> > Date: Mon, November 5, 2018 10:17 am > To: music-dsp@music.columbia.edu > -------------------------------------------------------------------------- > > > It's not exactly Cooley-Tukey. In Cooley-Tukey you take two _interleaved_ > > DFT's (that is, the DFT of the even-numbered samples and the DFT of the > > odd-numbered samples) and combine them into one longer DFT. But here > you're > > talking about taking two _consecutive_ DFT's. I don't think there's any > > cheap way to combine these to exactly recover an individual bin of the > > longer DFT. > > > > Of course it's possible you'll be able to come up with a clever frequency > > estimator using this information. I'm just saying it won't be exact in > the > > way Cooley-Tukey is. > > > > -Ethan > > > > > > > > -- > > 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 >
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