of Microprocessors

612 MUSICAL ApPLICATIONS OF MICROPROCESSORS
2. Amplitude is independently adjustable.
3. Phase is independently adjustable.
4. Amplitude and phase may be updated at any time without glitching
the output.
5. Fundamental frequency is controlled by a single 20-bit word.
6. The output is a 16-bit word at 62.5 ksls sample rate.
Much of the basic structure and organization of the previous multiplexed
oscillator will be retained. Thus, the Fourier series is evaluated via "brute
force" in which each harmonic is individually computed, scaled, and
summed. Although a computation time savings of 1O-to-1 is theoretically
possible through use of the FFT, the computation logic would be much more
complex. Also, as was seen in Chapter 13, FFT so/nthesis of arbitrary frequencies
(which is necessary in a fixed sample rate implementation) is even
more complex. Another advantage of brute-force evaluation is that amplitude
and phase changes take effect immediately, between samples, rather than
between FFT records.
Hardware Structure
Following the same development as before, Fig. 17-16 shows the
conceptual block diagtam of a single harmonic channel without multiplexing.
The first obvious feature is that three control variables are involved:
frequency, amplitude, and phase. Another feature is the inclusion of two
multiplier blocks, one for multiplying the frequency parameter by the harmonic
number and the other for multiplying the sine table content by the
amplitude variable. Phase control is implemented by adding the phase shift
parameter to the accumulator contents in a separate phase adder before feeding
it to the sine table. Finally, we have a harmonic accumulator, which sums the
output of this channel with that of the other harmonic channels to provide
the fina.l output, which is then sent to the DAC.
Before continuing further, a few things should be said about the word
lengths of the various blocks. When the 20-bit frequency control word is
multiplied by the 6-bit harmonic number, a 26-bit product is expected.
However, in order to use the same accumulator frequency generator and
sample rate as before, only the low order 20 bits of the product are used.
Thus, product overflow is possible when high fundamental frequencies are
used. While this may seem to be an operational restriction, a little thought
will reveal that product overflow is indicative ofserious alias distortion in the
tone anyway. When using the tone generator, the amplitudes of all harmonics
that exceed 31 kHz will have to be made zero. The word lengths in
the sine lookup blocks are 10 bits, the same as before. When 64 individual
sine waves are added up, the result is a 16-bit final output word.
Let's now look at these blocks and see how they would be implemented
in the multiplexed case. Since there are 64 harmonics, the amplitudes and