Consider the following problems related to steady state and frequency responses. (a) The input x(t)and the output y(t), x(t) = 4 cos(2Ï t) + 8

Consider the following problems related to steady state and frequency responses.

(a) The input x(t)and the output y(t),ˆ’ˆž

x(t) = 4 cos(2Ï€ t) + 8 sin(3Ï€ t), y(t) = ˆ’2 cos(2Ï€ t).

Determine as much as possible about the frequency response H(jΩ) of the filter using the above input and output.

(b) Given a LTI system with frequency response

If the input signal x(t)is periodic with Fourier series

calculate the steady-state response y_ss(t)of the system.

|-1/2 N > 0 |H(jN)| = u(N +2) – u(N – 2), ZH(jN)= T/2 N< 0 x(t) = D E cos(3kt/2) k=1