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.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada