The eigenfunction property is only valid for LTI systems. Consider the cases of non-linear and of time-varying systems. (a) A system represented by the input-output equation y(t) = x 2 (t) is non-linear. Let the input be x(t) = e jt/4 find the corresponding system output y(t). Does the eigenfunction property hold? Explain. (b) Consider a time-varying system y(t) = x(t) [u(t) u(t 1)]. Let x(t) = e jt/4 find the corresponding system output y(t). Does the eigenfunction property hold? Explain.

Question: The eigenfunction property is only valid for LTI systems. Consider the cases of non-linear and of time-varying systems. (a) A system represented by the input-output

The eigenfunction property is only valid for LTI systems. Consider the cases of non-linear and of time-varying systems.

(a) A system represented by the input-output equation y(t) = x²(t) is non-linear. Let the input be x(t) = e^jπt/4 find the corresponding system output y(t). Does the eigenfunction property hold? Explain.

(b) Consider a time-varying system y(t) = x(t) [u(t) − u(t − 1)]. Let x(t) = e^jπt/4find the corresponding system output y(t). Does the eigenfunction property hold? Explain.

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a If xt e jt4 is the nonlinear system input the output is yt x 2 t e jt2 which ca... View full answer

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