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LTI System

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Eigenfunctions and LTI systems

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 imput-output equation is nonlinear:
y(t) = x^2(t)
Let x(t) = e^(j*pi*t/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^(j*pi*t/4). Find the corresponding system output y(t). Does the eigenfunction property hold? Explain.

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