The impulse response of the system in Fig. 1.isand the input to the system is a periodic s...

The impulse response of the system in Fig. 1.is

and the input to the system is a periodic signal (with period T0 = 1) given by the equation

(a) Determine the Fourier transform X(jω) of the input signal. Plot X(jω) over the range –6π<ω < 6 π.

(b) Determine the frequency response H(jω) of the system and plot |H(jω)| on the same graph as X(jω) for the case ωco = 5π.

(c) Use your plot in (b) to determine y(t), the output of the LTI system for the given input x(t) when the cutoff frequency is ωco = 5π.

(d) How would you choose ωco so that the output is a constant; i.e., y(t) = C for all t. What is the constant C ?