Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.