The following problems relate to linearity, time-invariance, causality, and stability of discrete-time systems. (a) The output y[n]
Question:
(a) The output y[n] of a system is related to its input x[n] by y[n] = x[n]x[n ˆ’ 1]. Is this system
i. linear? time-invariant?
ii. causal? bounded-input bounded-output stable?
You may consider x[n] = u[n] as the input to verify your results.
(b) Given the discrete-time system in Figure 9.14
i. Is this system time-invariant?
ii. Suppose that the input is x[n] = cos (Ï€n/4), ˆ’ˆž < n < ˆž, so that the output is y[n] = cos (Ï€n/4) cos (n/4), ˆ’ˆž < n < ˆž. Determine the fundamental period N0 of x[n]. Is y[n] periodic? If so, determine its fundamental period N1.
Figure 9.14:
![x[n] y[n] (X) cos(n/ 4)](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/images/question_images/1545/4/9/3/7925c1e5d20dacc21545476368829.jpg)
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a i if input is xn the output is yn xn xn 1 if input is xn 1 the output is 2 x...View the full answer
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