Consider a discrete-time LTI system for which the frequency response H(ejω) is described...

Consider a discrete-time LTI system for which the frequency response H(e^jω) is described by:

(a) Is the impulse response of the system h[n] real-valued? (i.e., is h[n] = h∗[n] for all n)

(b) Calculate the following:

(c) Determine the response of the system to the input x[n] = s[n] cos(ω_cn), where 0 < ω_c < π/2 and S(e^jω) = 0 for ω_c/3 ≤ ω| ≤ π.