The following problems relate to linearity, time-invariance, causality, and stability of discrete-time systems. (a) The output y[n]
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(a) The output y[n] of a system is related to its input x[n] by y[n] = x[n]x[n 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 (Ïn/4), < n < , so that the output is y[n] = cos (Ïn/4) cos (n/4), < n < . Determine the fundamental period N0 of x[n]. Is y[n] periodic? If so, determine its fundamental period N1.
Figure 9.14:
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