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226 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
Columns 5 through 8
2.67651367187500 -1.52264404296875 0.28984069824219 0.49931716918945
>> hdir = filter(b,a,delta)
hdir =
Columns 1 through 4
0.06250000000000 -0.23437500000000 0.85546875000000 -2.28417968750000
Columns 5 through 8
2.67651367187500 -1.52264404296875 0.28984069824219 0.49931716918945
□ EXAMPLE 6.3 What would be the overall direct, cascade, or parallel form if a structure contains
a combination of these forms? Consider the block diagram shown in Figure 6.9.
□
Solution
This structure contains a cascade of two parallel sections. The first parallel
section contains 2 biquads, while the second one contains 3 biquads. We will have
to convert each parallel section into a direct form using the par2dir function,
giving us a cascade of 2 direct forms. The overall direct form can be computed
by convolving the corresponding numerator and denominator polynomials. The
overall cascade and parallel forms can now be derived from the direct form.
MATLAB script:
>> C0=0; B1=[2 4;3 1]; A1=[1 1 0.9; 1 0.4 -0.4];
>> B2=[0.5 0.7;1.5 2.5;0.8 1]; A2=[1 -1 0.8;1 0.5 0.5;1 0 -0.5];
>> [b1,a1]=par2dir(C0,B1,A1)
b1 =
5.0000 8.8000 4.5000 -0.7000
FIGURE 6.9 Block diagram in Example 6.3
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