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 a band limited with a frequency max( max) = 2000*pi rad/sec. Determine if y(t) is also a 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 c = 5000*pi rad/sec. Determine the value of the sampling period Ts according to the given information.
c. Is there a different value for Ts that would satisfy the Nyquist sampling rate condition for both x(t) and y(t) and that is larger than the one obtained above. Explain.