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Difference Equations 49
Solution
From the given difference equation the coefficient arrays are
b = [1]; a=[1, -1, 0.9];
a. MATLAB script:
>> b = [1]; a = [1, -1, 0.9]; n = [-20:120];
>> h = impz(b,a,n);
>> subplot(2,1,1); stem(n,h);
>> title(’Impulse Response’); xlabel(’n’); ylabel(’h(n)’)
The plot of the impulse response is shown in Figure 2.9.
b. MATLAB script:
>> x = stepseq(0,-20,120); s = filter(b,a,x);
>> subplot(2,1,2); stem(n,s)
>> title(’Step Response’); xlabel(’n’); ylabel(’s(n)’)
The plot of the unit step response is shown in Figure 2.9.
c. To determine the stability of the system, we have to determine h(n) for all n.
Although we have not described a method to solve the difference equation,
1
Impulse Response
0.5
h(n)
0
−0.5
−1
−20 0 20 40 60 80 100 120
n
Step Response
2
1.5
s(n)
1
0.5
0
−0.5
−20 0 20 40 60 80 100 120
n
FIGURE 2.9 Impulse response and step response plots in Example 2.11
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