of Microprocessors

PERCUSSIVE SOUND GENERATION 541
exciting the filter for results. Although an analog nonlinearity using diodes is
quite possible (and an interesting experiment), with the digital equivalent an
equation or table describing the transfer function can be used instead.
Not just any randomly chosen curve will work for the transfer function,
however. In order for the oscillation to die out completely, the slope of the
curve must always be positive. If the slope tends to increase away from zeta as
in Fig. 15-7A, the oscillation frequency will decrease as it dies out and
vice versa. Symmettical transfer functions lead to odd harmonics only while
nonsymmetrical ones give all harmonics. The position (low-pass) output of
the vibrator tends to have a very strong fundamental relative to the harmonics.
The velocity (bandpass) and acceleration (high-pass) outputs have
greater harmonic content.
The position feedback path is not the only one that can be made
nonlinear. The velocity path may also be nonlinear with the general effect of
distorting the decay envelope. Any of the amplifiers in the vibrator structure
can also be made nonlinear. For example, making the value of FCl dependent
on position means that the vibrating mass depends on position such as in the
vibrating ruler case. (The reader should be aware that the ruler sound cannot
be duplicated with just the nonlinear oscillator; the impact of the ruler
hitting the table excites additional resonances in the ruler that require
additional filters to simulate.) It is important to note that digital simulations
of nonlinear vibrators can easily generate frequencies above one-half the
sample rate. Thus, experiments should be done at fairly low resonant frequencies
and without sharp discontinuities in the nonlinear transfer functions.