ODP: Filters

[Sean Costello]

Brigman, Corley wrote:

> the main problem with the FFT-based implementation is, afaik, that each
> "window"  of the FFT don't have a 1:1 correspondence to frequency. i.e.: at 
> 44.1KHZ, if  you take a sample of 512 samples, then each sample corresponds to 
> approx. 43 HZ (iirc) and I THINK it is linear?? can't remember for sure.
> increasing the window size helps, but for each band you are increasing/decreasing > a frequency RANGE and not a frequency per se - i guess this is why you have the 
> "harmonic" problems? 

OK, this is an area I am not too comfortable with yet, but I have done a
little reading. ("I'm not a doctor - but I watch a lot of TV.")  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.  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.  Various other nifty techniques can be applied - for
example, SMS analysis (developed by Xavier Serra during his stint at
CCRMA) analyses a signal and breaks it down into sinusoids plus a
"residual" of filtered noise.  I think this is done by assuming that
components in the frequency bins that are slowly changing are the
sinusoidal components of the signal, while components that change
amplitude and phase rapidly are better described as "noise."

BTW, I am planning on taking some EE courses soon, so I should hopefully
know what the hell I am talking about soon.  The computer music course I
am taking is cool, but the teacher doesn't have time to get into the
technical nitty-gritty. He certainly knows how to do it (he developed
time strecting and phase vocoding opcodes for Csound), but the class has
to be tailored towards the music composition students.  Time to squeeze
into those EE classes.

Sean Costello

"I'm not a doctor - but I'm Charles Manson."