[music-dsp] waveshapers and DC-offset

Olli Niemitalo oniemita at mail.student.oulu.fi
Mon Aug 21 03:16:21 EDT 2000


On Mon, 21 Aug 2000, Laurent de Soras wrote:

> A second order polynomial will ensure that the output
> signal is band-limited with a maximum frequency at
> f1 = 2*f0, where f0 is the maximum frequency contained
> in the input signal. A 2 x oversampling (or low-pass pre-
> filtering at fs/4) will be enough to avoid aliasing.

This is interesting... :)

The output of a polynomial waveshaper is actually just a weighted sum of
these primary waveshapers:

Waveshaper:     Bandwidth:
1               0 (DC only!)
input(T)        Nyquist (obvious!)
input^2(T)      2 Nyquist
input^3(T)      3 Nyquist
...             ...

The bandwidths of each can be determined by thinking of the multiplication
operation, as in input^2(T) = input(T)*input(T)), as frequency domain
convolution.

-olli


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