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Digital Sound & Music: Concepts, Applications, & Science, Chapter 7, last updated 7/29/2013
Another way to create and apply an IIR filter in MATLAB is by means of the function
yulewalk. Let's try a low-pass filter as a simple example. Figure 7.43 shows the idealized
frequency response of a low-pass filter. The x-axis represents normalized frequencies, and f_c is
the cutoff frequency. This particular filter allows frequencies that are up to ¼ the sampling rate
to pass through, but filters out all the rest.
Figure 7.43 Frequency response of an ideal low-pass filter
The first step in creating this filter is to store its "shape." This information is stored in a pair of
parallel vectors, which we'll call f and m. For the four points on the graph in Figure 7.44, f stores
the frequencies, and m stores the corresponding magnitudes. That is,
and
, as illustrated in the figure. For the example filter we have
f = [0 0.25 0.25 1];
m = [1 1 0 0];
Figure 7.44 Points corresponding to input parameters in yulewalk function
 Aside: The yulewalk function in MATLAB is
named for the Yule-Walker equations, a set of
linear equations used in auto-regression
modeling.
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