7. Let a[n] and y[n] be the input and output of a discrete-time system, respectively, and...
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7. Let a[n] and y[n] be the input and output of a discrete-time system, respectively, and they are related by y[n] = -ay[n-1] + a[n]. Suppose r[n] = u[n] which is the unit step function and y[-1] = 0. Answer the following: (a) (b) Use MATLAB to generate and plot y[n] for 0 ≤ n ≤ 100 with a = 0.5. What is the value of y[10]? Do you think that the system is stable? Why? Use MATLAB to generate and plot y[n] for 0 ≤ n ≤ 100 with a = 2. What is the value of y[10]? Do you think that the system is stable? Why? 7. Let a[n] and y[n] be the input and output of a discrete-time system, respectively, and they are related by y[n] = -ay[n-1] + a[n]. Suppose r[n] = u[n] which is the unit step function and y[-1] = 0. Answer the following: (a) (b) Use MATLAB to generate and plot y[n] for 0 ≤ n ≤ 100 with a = 0.5. What is the value of y[10]? Do you think that the system is stable? Why? Use MATLAB to generate and plot y[n] for 0 ≤ n ≤ 100 with a = 2. What is the value of y[10]? Do you think that the system is stable? Why?
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