ODP: Filters

[Brigman, Corley]

First, i also am still learning this, so i won't guarantee anything i say to
be 
correct :) but at least i believe it to be correct...it's been a couple
years, 
and i didn't know it well then....

>The
>phase vocoder resolves this problem by tracking the phase of each
>frequency bin in the FFT, and using the change in phase for each window
>to determine the actual frequency. 

fft's don't have to be complex, there is a simplification (i forget what it
is) 
or a certain type of signal that most signals fall into that mean the
complex 
part is all 0 i.e. all real. i'd be interested to hear more about why the
phase 
information is needed. in my (admittedly short) analyses, for an ADDITIVE
synth 
(not fourier-based, but they are similar), the phase is unimportant - the 
waveform is quite different, but the sound is the same. the FFT guarantees 
sample accuracy, of course, so it's a little different. my testing was for 
relatively simple waveforms though - square and saw. if you want to try it,
the 
additive engine at my homepage http://members.xoom.com/elev8 lets you play
with 
this. I tried both shifting all harmonics by, say, 90 degrees, as well as 
shifting different harmonics different amounts. They will probably be
different 
when played polyphonically, maybe, but the basic sound was the same to my
ears. 
This would follow from the above simplification. I believe the
simplification is
for finite, deterministic signals or something like that. looks like it's
time 
to crack open the book again.

> A phase vocoder can analyse a sound,
>and perfectly reconstitute the sound from the analysis material,
>provided that no changes have been made in between analysis and
>resynthesis. 

this is a direct property of the DFT, as i recall, in both discrete and 
continuous forms. as far as I know, though, you don't need a complex FFT for

this relation to be true - can anyone correct me? I throw this stuff out as
much
to learn as anything....phase vocoding is a good way to pitch shift though, 
since it maintains the harmonic relationships of the source signal (at
least, 
IIRC). at least it's an easier way to get right. to do proper phase vocoding
i 
suppose you need an exponential FFT, i think these exist but I wouldn't
swear to
it....you could "fake" it coarsely using a linear FFT of course.

enjoying this discussion,

corley brigman
intel corp.
corley.brigman at intel.com

speaking for me, not for intel.