[PD] mathematician types (was: Big distortion ?)

[Mathieu Bouchard]

On Mon, 17 Apr 2006, Charles Henry wrote:

> Is there a spectral theory of waveshapers?  Generally speaking,
> distortion produces different harmonics of signals.... Another way of
> generating harmonics is to use convolution in the fourier domain... for
> example, the nonlinear transfer function y=x^3 can be represented in the
> fourier domain: FT(y)= FT(x) convolved with FT(x) convolved with FT(x)

There is a spectral theory of waveshapers, but you never hear about it 
because it's just the spectral theory of convolution read backwards. Try 
turning your book upside down...

> and curiously....we can compute and convolve fractional powers of the FT...

Yeah, I tried fractional convolutions last week. I tried applying this
effect on video, and it gives some *really* cool results if tuned
appropriately. With Pd of course.

btw there's also a thing called fractional fourier transform, but that's a
different beast, it's double extra weird. It maps the time domain to the
cos(a)*time+sin(a)*frequency domain for a value "a" of your choice. 
unfortunately I have no clue what that means and I think it only works on 
paper.

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada