[sdiy] Speaking of the Elektor Vocoder (and the Korg Vocoder)

[Eric Brombaugh]

anthony wrote:
> 
> I suppose a filter-bank could be thought of as a crude or coarse FFT. 
> The more and narrower the filterbanks the more it would come to 
> approximate an FFT - maybe in this case FT. Well actually, doing it 
> analog, it's sort of instantaeous. But I wonder if the transfer function 
> of a bunch of filter banks has the same math behind it as the actual  
> Fast Fourier Transform, which as I understand it, is a recursive algorithm.
> 
> Math guys?

Not really a math guy, but I'll take a stab at it. :)

In general, no. Specifically, it depends on what kind of filter bank 
you're talking about.

An FFT is a specific algorithm for implementing the Discrete Fourier 
Transform (DFT) which optimizes the number of multiply/adds required. In 
order to support the optimization, the FFT imposes certain limits on the 
amount of data you transform (although there are tricky ways to expand 
the possible data sizes). The FFT is an iterative (but not recursive) 
algorithm - the number of iterations depends on the data size.

The underlying math of the DFT is very different from the processing 
that's taking place in a typical analog filter. A closer analogy to DFT 
processing would be more like what happens in a radio receiver.

The DFT can be though of as a filter bank, but it has the property that 
all the filters have the same bandwidth and are centered on integer 
multiples of the fundamental frequency, which is determined by the size 
of the transform. I haven't studied vocoders, but I don't think that 
they necessarily have these properties. I would imagine that analog 
Vocoders would more likely use filters that have constant shape factor 
(bandwidth increases with increasing frequency - like 1/3 octave 
filters). An DFT-based vocoder would tend to give you more resolution at 
higher frequencies where the human ear doesn't really need it.

As an aside, I'm interested that analog processing is 'sort of 
instantaneous', while digital processing is apparently not. Where does 
this belief come from?

Eric