[music-dsp] Hi list -- some questions

Sampo Syreeni decoy at iki.fi
Mon May 12 15:46:56 EDT 2003

On 2003-05-12, Russell Borogove uttered to music-dsp at aulos.calarts.edu:

>If you're very partial to sinh(), x + (0.2*x*x*x) is a decent
>approximation to it over the -1 to +1 domain.

Also, don't forget Horner: x+0.2*x*x*x = x(1+0.2*x*x). Might just save you
a multiply, every now and then, and it doesn't hurt that it also tends to
be a bit stabler with high order polynomials.

>It blows up fast at larger magnitudes, though not as fast as sinh does,
>for which reason many people prefer shapers of the form x-(k*x*x*x)
>instead of x+(k*x*x*x) - similar harmonic structure, but with a tendency
>to limit the output magnitude in moderate overdrive situations.

We should also remember polynomials give rise to bandlimited waveforms
(not limited to the current Nyquist, but a multiple by the order of the
polynomial). Predicting how they behave when oversampling is much easier
than with hyperbolic functions and such -- there you have to rely on power
series representations and approximate, while straight powers give you
precisely what you want, with a neatly determined, integral oversampling
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2

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