a) Show (prove) that the signal 3^j2t is an eigenfunction of any LTI system, and nd the formula for the eigenvalue. That is, use the convolution integral and simplify to show that if you input 3^j2t into an LTI system with impulse response h (t ), then the output is 3^j2t multiplied by some scalar that does not depend on time (this scalar is the eigenvalue corresponding to this eigenfunction).
b) What is the formula for the eigenvalue from part (a)?
c) If h (t ) = d(t - 7) + d(t + 7), calculate the eigenvalue for the system, putting your answer in the form a cos(b ).