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# Eigenfunctions and LTI systems

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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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#### Solution Preview

Hello,

This problem is related to the linear system theory. So, i will just explain some points for your revision here. Please note that, the eigenfunctions and the basis functions of the transforms, are complex exponentials for all LTI systems. This means that, if the input to a system is the complex waveform Ae^(st) for some complex amplitude A and complex frequency, (s), the output will be some complex constant times ...

#### Solution Summary

This solution provides two examples of systems for which eigenfunction property is evaluated.

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