The eigenfunction property is only valid for LTI systems. Consider the cases of nonlinear and of time varying systems.
(a) A system represented by the following input-output equation is nonlinear:
y(t) = x2(t)
Let x(t) = ejpt/4. Find the corresponding system output y(t). Does the eigen function property hold? Explain.
(b) Consider a time-varying system
y(t) = x(t)[u(t) - u(t - 1)]
Let x(t) = ejpt/4. Find the corresponding system output y(t). Does the eigen function property hold? Explain.