of Microprocessors

52 MUSICAL ApPLICATIONS OF MICROPROCESSORS
OUTPUT
WAVE
10
~ 0
~ -10
=>
:s -20
0-
~ -30
-40
-50 .L.......L.~-'-L-L-:'::--':-'-L-:-'---:!~---':--,':-J-.,........,..,~==--
INPUT SINE WAVE
1D)
SPECTRUM
Fig. 2-2. Nonlinear waveshaping (cant.). (D) Half~wave rectification with
offset.
fundamental at twice the frequency. Figure 2-2F shows the result of varying
two possible parameters of the transfer curve; a center clipping threshold and
the slope (gain) for positive input signals.
Actually, pure sine waves are seldom used as the source signal such as
when a musical instrument's sound is being modified. Depending on the
exact waveform, a given nonlinearity may increase some harmonics, reduce
others, and leave some generally unchanged. Instrumental waveforms are not
constant either. Frequently, slight changes in input waveform (from sliglit
harmonic phase changes, for example) may result in large changes in output
spectrum. One interesting waveform that is not affected by any kind of
nonlinear device is the square wave. Although the amplitude may be
changed, the square waveshape is never altered.
Of course, there are literally thousands of possible nonlinear curves,
each with a set of parameters that may be changed to vary the output signal
spectrwn. There are important drawbacks to their use, however. One drawback
is that the relationship between a parameter or parameters describing a
certain class of transfer curves and the actual spectrum in terms of harmonics
is not always simple. For example, increasing a dipper parameter may at
first give increased high harmonic content, but further increases of the same
parameter might actually reduce the high harmonics or shift the emphasis
to middle harmonics. The situation gets much more complicated if a
complex waveform is used for the input.
Another important drawback is that nonlinear devices generally give
desirable results only with single tone inputs. If two simultaneous tones of