Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
Figure 2.29 Adding sound waves in Pure Data
2.3.3 Modeling Sound in MATLAB
It's easy to model and manipulate sound waves in MATLAB, a mathematical modeling program.
If you learn just a few of MATLAB‟s built-in functions, you can create sine waves that represent
sounds of different frequencies, add them, plot the graphs, and listen to the resulting sounds.
Working with sound in MATLAB helps you to understand the mathematics involved in digital
audio processing. In this section, we'll introduce you to the basic functions that you can use for
your work in digital sound. This will get you started with MATLAB, and you can explore
further on your own. If you aren't able to use MATLAB, which is a commercial product, you
can try substituting the freeware program Octave. We introduce you briefly to Octave in Section
2.3.5. In future chapters, we‟ll limit our examples to MATLAB because it is widely used and
has an extensive Signal Processing Toolbox that is extremely useful in sound processing. We
suggest Octave as a free alternative that can accomplish some, but not all, of the examples in
remaining chapters.
Before we begin working with MATLAB, let‟s review the basic sine functions used to
represent sound. In the equation ) Asin(2fx y , frequency f is assumed to be measured in
Hertz. An equivalent form of the sine function, and one that is often used, is expressed in terms
of angular frequency, , measured in units of radians/s rather than Hertz. Since there are
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