of Microprocessors

14
DigitalFiltering
In analog synthesis, filtering is used almost exclusively for modification of
the severely limited oscillator waveforms available. However, as was just
discussed, digital oscillators and tone generators are considerably more flexible
and are themselves capable of virtually any spectral effect desired.
Nevertheless, tone modification by filtering is still an important technique if
for no other reason than convenience. In the digital domain, such modification
may be achieved directly by giving each harmonic its own amplitude
envelope, thereby simulating the effect of a varying filter. However, use ofan
actual filter may require far fewer varying parameters to achieve the desired
result. This is particularly true if the user has had experience with analog
systems because the desired result will usually be thought of in terms of
filtering.
Also, some types of sounds require the use of filters in their synthesis.
For example, it is difficult to generate "random" noise with a specified
frequency spectrum directly; however, one or more filters can easily shape a
flat noise spectrum into what is required. Also, in sound modification applications
in which one has no direct control over the source material, filtering
is the only reasonable way to modify the spectrum. Frequency-sensitive time
delay (dispersion) and frequency-sensitive phase shift are functions that are
useful in chorus and reverberation simulators and that are normally regarded
as "all-pass" filtering. Finally, as we shall see in the next chapter, digital
filter ringing is a very convenient method for generating percussive sounds.
Just as a digital oscillator can generate any waveform subject to the
constraints ofsampling, a digital filter can be designed to have any frequency
and phase characteristic qesired with only two limitations. One is the highfrequency
limit imposed by sampling. For example, a digital high-pass filter
cannot be expected to provide a high-pass characteristic up to infinity like an
ideal analog filter would. Instead, the response is undefined beyond one-half
the sample rate and may be distorted somewhat just below one-half the
sample rate. Another limitation is that filters cannot be expected to predict
the future! While this may seem obvious, a low-pass filter specifimtion with
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