of Microprocessors

120 MUSICAL ApPLICATIONS OF MICROPROCESSORS
modification by means of filtering can be accomplished with digital jilters,
Actually, a digital filter is nothing more than an equation that specifies the
Nth output sample as a function of several previous input samples and some
filter response parameters. A special case is the recursive digital filter, which
only uses the previous output sample and the current input sample along
with response parameters to produce an output sample. All of the common
filter amplitude response shapes such as low-pass, bandpass, and high-pass
are easily done with recursive digital filters. Arbitrary response shapes can
also be done in a straightforward manner with nonrecursive digital filters.
Calculation time is longer with these, since several up to several hundred
previous input samples are evaluated to produce the output but the response
shapes produced would be very difficult to duplicate with recursive digital or
analog filters. As with all other direct synthesis techniques, there is no real
limit to the number of digital filters that may be in use simultaneously.
Usually the programming is done with a small group of routines for the
different general types of filters and then the characteristics of specific filters
in use at the time are simply numbers stored in a table in memory.
Reverberation and chorus effects previously described are also easily
done. One of the simplest operations in a direct synthesis system is delay. All
that is required for delay is a memory buffer and a simple program for storing
current samples into and withdrawing delayed samples from the buffer. Very
little computation time is required for a delay function, although the buffer
memory could become substantial for long or multiple delays. Delay times
are easily varied in whole sample increments and interpolation may be used
for even finer increments. Thus, all methods for reverberation and chorus
may be applied directly and even refined considerably. If time is no object,
the characteristics of a particular concert hall may be duplicated using only
the waveform of a spark discharge (or other repeatable sharp sound) recorded
in the actual hall for input.
The tape-splicing methods covered earlier can be done also and with
great efficiency. Generally, the computer system should have a large disk
storage facility for quick access to a library of recorded natural and synthetic
sounds. The largest part of such a sound-editing system is simply the bookkeeping
needed to keep track ofsound fragments in various stages of completion.
The actual cutting and splicing operations could be done at a graphic
display console showing actual waveforms or spectra with a light pen to
specify the cut or splice points.
One modification technique that does not always work well when done
digitally is nonlinear waveshaping. Since clipping and other waveshape distortions
are likely to generate strong high-frequency harmonics, alias distortion
can become a problem. If necessary, the distortion operation can be done
at a much higher sample rate at which the alias distortion is less of a
problem, then digitally low-pass filtered to less than half of the system
sample rate, and finally resampled. Fortunately, such gross distortion techniques
are seldom needed when more refined techniques are available.