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) and curiously....we can compute and convolve fractional powers of the FT... I haven't gone too far in depth for this hypothesis....just a thought for you mathematician types, heh heh
Chuck
On 4/16/06, Tim Blechmann TimBlechmann@gmx.net wrote:
On Sun, 2006-04-16 at 16:16 -0400, Mathieu Bouchard wrote:
And about waveshaping, let me say that, for "big distortion", in addition to the tanh(x) and atan(x)*2/pi functions that I may have previously mentioned, x/sqrt(1+x*x) and erf(x) are quite cool. They aren't particularly modeling the behaviour of analog amps nor speaker membranes, but still, they're rather simple functions that appear everywhere in science.
well, most cumulative distribution functions can be adapted as wonderful wave-shapers .... with the right preamplification and paramerers they make really powerful tools ...
t
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