[sdiy] Fourier Analysis Question

[Richard Wentk]

There are various approaches to dynamic interpolation. A lot of them require phase/frequency partial tracking and interpolation. 

But they all have the same problem - if you're doing windowed resynthesis with FFTs, you need to add an extra stage of windowed overlap to get a smooth sound. 

This means you literally have to do n^2 extra FFTs, and then crossfade between the time domain output using another windowing function. Suddenly the F in FFT doesn't look quite as F as it used to. 

FFTs only really work as a one to one if you do direct synthesis/resynthesis. As soon as you transform the data in any way at all, you typically need to do at least eight times more work to get a smooth-sounding result. 

So it makes more sense to use a more general model that produces timed and keyframed partial frames for analysis, and discrete oscillators for resynthesis, with interpolation between the keyframes. 

It's worth playing with this stuff in Csound, because it's a nice (relatively) simple testbed for experiments.

For dynamic analysis you can also use wavelets which naturally support variable window lengths. 

But that's where things get complicated. (Too complicated for me to experiment with, anyway.)

R

On 18 Dec 2010, at 01:56, Scott Nordlund wrote:

>> The Robert Bristow-Johnson paper I mentioned earlier discusses this- if you preserve phase information but ensure that it's continuous between timbre frames, you can get anharmonic partials with a piecewise linear approximation of the original relative phase shift. Of course, this will change if you choose to traverse through the wavetable at a different rate.  Anyway I think one of the main advantages is that with some effort, you can do completely smooth interpolation for velocity and keyboard zones.
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