Question: The input/output relation of a non-linear system is y(t) = x 2 (t), where x(t) is the input and y(t) is the output. (a) The

The input/output relation of a non-linear system is y(t) = x²(t), where x(t) is the input and y(t) is the output.

(a) The signal x(t) is band-limited with a maximum frequency Ω_M = 2000π(rad/sec), determine if y(t) is also band-limited and if so what is its maximum frequency max.

(b) Suppose that the signal y(t) is low-pass filtered. The magnitude of the low-pass filter is unity and the cut-off frequency is Ω_c = 5000π(rad/sec), determine the value of the sampling period T_s according to the given information.

(c) Is there a different value for T_s that would satisfy the Nyquist sampling rate condition for sampling both x(t) and y(t) and that is larger than the one obtained above? Explain.

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