mr. g,I think what you're describing is the Cooley-Tukey Radix-2 FFT 
algorithm.--r b-j           "Imagination is 
more important than knowledge."

-------- Original message --------
From: gm <> 
Date: 11/4/2018  4:14 PM  (GMT-08:00) 
Subject: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime

bear with me, I am a math illiterate.I understand you can do a Discrete Fourier 
Transform in matrix form,and for 2-point case it is simply[ 1, 1   1,-1]like 
the Haar transform, average and difference.My idea is, to use two successive 
DFT frames, and to transform resepctive bins of two successive frames like 
this.To obtain a better frequency estimate (subbands) from two smaller DFTs 
instead of an DFT double the size.This should be possible? and the information 
obtained, time and frequency resolution wise, identical.Except that you can 
overlap the two DTFs.I basically want to find the dominant frequency in the FFT 
bin, and sepreate it and discard the rest.And a subband resolution of 2 seems 
to be a sufficient increase in resolution.But how do I get that from this when 
there is no phase other then 0?I can see which of the two bands has more 
energy, but how do I know "the true frequency" of Nyquist and DC?There is not 
enough information.The problem persists for me if I resort to a 4-point 
transform, what to do with the highest/lowest subband.(and also to understand 
how to calculate the simple 4 point matrix, cause I am uneducated..)Or do I 
need the 4-point case and discard "DC" and Nyquist subbands?Or is the idea 
totally nonsens?Or is it justified to pick the subband that has more energy, 
and then, what?_______________________________________________dupswapdrop: 
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