of Microprocessors

DIGITAL HARDWARE 603
As an example, consider the synthesis of a tone having the exact harmonic
makeup (chosen at random) listed in Table 17-1. For the sake of
argument, let's assume that only 64 words of memory (64 samples per cycle)
are available and that each word is a paltry 6 bits long, which means that a
6-bit DAC can be used. Also shown in Table 17-1 are the corresponding
sample values to 16-bit (5-digit) accuracy and rounded to 6-bit accuracy. The
final column shows the actual harmonic spectrum that would emerge from
this low-budget tone generator.
The first surprise is that the difference between desired and actual
harmonic amplitudes expressed in decibels is not very great, at least for the
significant high-amplitude ones. Lower-amplitude harmonics do suffer
greater alteration but are more likely to be masked by the higher-amplitude
harmonics. The real difference is that no harmonic can be entirely absent
because of the quantization "noise." In actual use with a fairly "bright"
harmonic spectrum, the approximation errors would be audible but would be
characterized as a slight timbre alteration rather than distortion; much like
the audible difference between two presumably excellent speaker systems of
different manufacture. The use of 8 bits and 256 steps for the waveform of a
digital oscillator is therefore well justified.
Although the alias frequencies are also harmonic, they should be filtered
if a high-pitched "chime" effect is to be avoided. Unfortunately, the
filter cutoff must track the tone frequency as it changes. This used to be an
expensive proposition but ~ 2040 VCF driven by an 8-bit DAC connected to
the frequency control word can now solve the problem for under $15. In
many cases, it may be possible to omit the filter. For example, when using a
256-entry waveform table, only fundamental frequencies below 150 Hz require
filtering, since otherwise the alias frequencies are entirely beyond 20
kHz. In fact, meilow tones containing few harmonics can be generated
filter-free down to 80 Hz.
A dedicated digital tone generator can, of course, be based on the
constant sample rate approach too. The structure is basically the same as
Figs. 17-9 and 17-'-10 except for the following:
1. The master clock (sample rate) is much slower, such as 50 ks/s.
2. The most significant bits of the accumulator divider will be actual
register bits, since the slow clock eliminates the "jitter-filter"
counter (the jitter now becomes interpolation error).
3. The waveform memory will require more words (1,024) and more
bits per word (10-12), since interpolation and quantization error
will now be white noise instead of pure harmonic distortion.
The constant sample rate tone generator is, in fact, a precise hardware
implementation of the software table-scanning technique described in
Chapter 13. In exchange for additional hardware complexity, one has a
structure that can use a fixed low-pass filter (probably no filter at all for 50-