of Microprocessors

544 MUSICAL ApPLICATIONS OF MICROPROCESSORS
always be the most efficient or most accurate techniques, they get the job
done. It is much more important for the beginner to actually do some
analysis programming and see the results than to have a thorough mathematical
understanding of the underlying principles. Only two types of analysis
will be described in detail. The first is generalized spectrum analysis in
which the time-varying spectrum of the source sound is determined. The
second concentrates on extracting and following the frequency parameter of a
changing sound, a very useful function.
Spectrum Analysis
Most source-signal analysis begins with spectral analysis, since virtually
everything that is audible and important about a sound shows up vividly in a
spectral analysis. The results of the analysis may then be plotted, passed
directly to a synthesis process, or undergo further processing.
A time-variable spectral plot, which is also called a short-time spectral
analysis, is actually a three-dimensional "surface" that shows the relation
between time, frequency, and amplitude variables. Time and frequency are
the independent variables, while amplitude is the dependent variable. When
spectra are computed digitally, all three variables are quantized and two of
them, amplitude and frequency , are also sampled. In effect the "volume"
represented by the allowable ranges of these variables is filled with discrete
points and the spectral surface is defined only at point intersections.
Plotting Methods
Obviously, most computer graphic displays and plotters cannot directly
show a three-dimensional surface. This shortcoming has resulted in at
least five distinct methods of representing the data on paper or a CRT screen.
Perhaps most obvious is an isometric drawing of the surface such as illustrated
in Fig. 16-1A. The surface is drawn in a horizontal position with
peaks and valleys much like a land area relief map. Typically, time runs
north/south, while frequency runs eastlwest, although they may be interchanged.
Height always represents amplitude. Such a representation gives a
"spectacular view" of the spectrum to say the least but is very difficult to
draw, since hidden line removal (the surface is opaque instead of transparent)
is necessary to avoid clutter.
A somewhat easier-to-draw representation consists of a stack of standard
two-dimensional curves such as illustrated in Fig. 16-1B. Each curve
represents a standard amplitude-versus-time plot at a particular frequency.
Therefore, the horizontal axis is time and the vertical axis is amplitude. Each
graph is displaced vertically upward as well so the vertical axis is also frequency.
Sometimes the curves are skewed to the right as well as upward to
give an isometric effect.
A third method, which is particularly applicable to digital spectra,
approaches a true three-dimensional representation more closely. With a