of Microprocessors

DIRECT COMPUTER SYNTHESIS METHODS 111
Recently, variations of the system shown in Fig. 4-4 have been used in
ordinary sound record/playback applications. The "compact disk" digital
audio playback system, for example, breaks the block marked "computer" in
half but is otherwise the same. The left half becomes a digital modulator (to
encode digital information onto an RF carrier wave) and laser scriber to
produce a modified type ofvideo disk. The right half becomes a laser scanner
to recover the modulated RF carrier wave and a demodulator to recover the
digital information, which is then passed on as before. Similar systems using
a video cassette recorder in place of the laser disk are also available. Such
systems far surpass regular analog disks and tapes in reproduction fidelity,
thus further emphasizing the fact that any sound can be synthesized by a
direct synthesis system.
The foregoing has all been an application of Nyquist's theorem, which
states in mathematical terms that an ADC or a DAC can handle signal
frequencies from zero up to a little less than one-half the sample rate with
absolutely no distortion due to the sampling process whatsoever. The lowpass
filters employed to separate the desired signal from the spectrum copies
determine how close to the theoretical one-half limit one can get. The main
requirement of the filter is that it attenuate spurious signals above one-half
the sample rate enough to be ignored while leaving desired signals below
one-half the sample rate unaltered. For high-fidelity applications, this means
that very little attenuation offrequencies up to 20 kHz is allowed and that 50
dB or more attenuation above 30 kHz is desirable, assuming a 50-ks/s sample
rate. A filter that sharp is fairly difficult to construct but is in the realm of
practicality. Thus, a rule of thumb is that the sample rate should be 2.5 or
more times the maximum signal frequency of interest with the larger figures
allowing simpler filters to be used. This is shown in Fig. 4-3B, in which an
increase in sample rate from 50-ks/s to 60-ks/s has reduced the filter cutoff
slope requirement by half!
The sample rate may also be reduced for lower fidelity applications. The
laser-disk- and videotape-based digital audio systems mentioned earlier
operate at slightly over 44 ks/s. Broadcast FM quality may be obtained at
37.5 ks/s and ordinary AM radio quality (which can be surprisingly good
through decent equipment) could be done at 15 ks/s to 20 ks/s. The
advantage of lower sample rates, of course, is a reduction in the number of
samples that must be computed for a given duration of sound.
Signal-to-Noise Ratio
Of course, frequency response is not the only measure of sound quality.
Background noise is actually a much worse problem with standard analog
audio equipment. Figure 4-1C clearly indicated that the sampling process
itself did not introduce any background noise. However, when the samples
are in numerical form, only a finite number of digits is available to represent
them, and this limitation does indeed introduce noise. Such roundoff error is