Sampling output of nonlinear system The input output relation of a non-linear sy

Question

Sampling output of nonlinear system
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.

Explanation / Answer

a. y(t) contains dc as well as 2nd harmonic corresponding to all frequency components in x(t). So max frequency in y(t) with out any filtering is band limited with 4000*pi rad/sec.

b. Here filter frequency is 5000*pi rad/sec, so sampling frequency would be 10000*pi rad/sec, so corresponding ampling period is 1/5000 sec.

c. 1/5000sec is enough because it covers both x and y, in general when you have to sample two signals so sampling rate corresponding to max frequency is enoguh.

Thanks,

Raj.

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