Well, I dunno shit about the history also.  I just ascribed all of the radix-2 
FFT to Cooley and Tukey.But I think you're mistaken about the technical claim.  
If you have or can get Oppenheim and Schafer and go to the FFT chapter of 
whatever revision you have, and there are several different 8 point FFTs that 
they illustrate.--r b-j                     
r...@audioimagination.com"Imagination is more important than knowledge."

-------- Original message --------
From: Ethan Fenn <et...@polyspectral.com> 
Date: 11/5/2018  11:34 AM  (GMT-08:00) 
To: robert bristow-johnson <r...@audioimagination.com>, 
music-dsp@music.columbia.edu 
Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime 
synthesis? 

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!)-EthanOn 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."
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