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Another interesting class of waveshaping transfer functions is the sinusoids:
which include the cosine and sine functions (got by choosing and
, respectively). These functions, one being even and the
other odd, give rise to even and odd harmonic spectra, which turn out to be:
The functions are the
Bessel functions
of the first kind, which
engineers sometimes use to solve problems about vibrations or heat flow on
discs. For other values of , we can expand the expression for :
so the result is a mix between the even and the odd harmonics, with
controlling the relative amplitudes of the two. This is demonstrated in Patch
E07.evenodd.pd, shown in Figure 5.14.
Figure 5.14:
Using an additive offset to a cosine transfer function to alter the
symmetry between even and odd. With no offset the symmetry is even. For odd symmetry, a quarter cycle is added
to the phase. Smaller offsets give a mixture of even and odd.

Next: Phase modulation and FM
Up: Examples
Previous: Waveshaping using an exponential
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Miller Puckette
20061230