of Microprocessors

106 MUSICAL ApPLICATIONS OF MICROPROCESSORS
complexity of computers in general and programming in particular is being
overcome by easier to use computer systems and early introduction of programming
concepts. It is not unusual for elementary school students to
become very adept at programming using simplified languages. Hopefully,
books such as this will take some of the mystery out of the theoretical aspects
of direct computer synthesis. Even the critical mass problem is decreasing in
severity as the performance/price ratio of digital electronics seems to double
every year.
These improvements in technology coupled with inherent limitless
capability would seem to indicate that direct computer synthesis will eventually
oust all other methods in serious electronic music applications.
SoundinDi~twForm
Computers deal with numbers and sound consists of continuously varying
electrical signals. Somehow the two have to be accurately linked together
in order for direct computer sound 1tynthesis to work at all. Fortunately, this
is possible with fewer limitations than might be expected.
The first problem to be solved is how to represent a waveform that can
wiggle and undulate in a seemingly infinite variety of ways with a finite
string of numbers having a finite number of digits. Intuitively, one would
probably suggest dividing the time axis up into a large number of segments,
each segment being a short enough time so that the waveform does not
change very much during the segment. The average amplitude of the
waveform over each segment could then be converted into a number for the
computer or vice versa. It would seem that the accuracy of the approximation
could be made as good as desired by making the segments small enough.
Let us take an example and see how small these segments must be for
high-fidelity sound-to-numbers and numbers-to-sound conversion. Figure
4-IA shows a I-kHz sine wave that has been chopped into 100 segments per
cycle of the wave. The segment time is thus 10 J.tsec. Assuming that the
desire is to generate the sine wave given the string of 100 numbers repeated
continously, the problem is to determine how good it will be.
Digital-to-Analog Converter
First, however, a device to do the conversion is needed. Such a device is
called a digital-to-analog converter, which is usually abbreviated DAC. Such a
device accepts numbers one at a time from a computer or other digital source
and generates one voltage pulse per number with a height proportional to the
number. Thus, a DAC that is calibrated in volts would give a voltage pulse
2.758 V in amplitude ifit received a numerical input of 2. 758. The width of
the pulses is constant but varies with the type of DAC. For now, the pulse
width will be assumed to be very small compared to the spacing between
pulses.
Figure 4-IB shows the output from a DAC fed the 100 numbers
representing a I-kHz sine wave. As expected, it is a string of very narrow