Consider the cascade of two filters with frequency responses H 1 (j) = j, and H 2

Consider the cascade of two filters with frequency responses

H₁(jΩ) = jΩ, and H₂(jΩ) = 1e^−jΩ

(a) Indicate what each of the filters does.

(b) Suppose that the input to the cascade is

x(t) = p(t) cos(πt/2),       where p(t) = u(t + 1) − u(t − 1)

and the output is y(t). Find y(t).

(c) Suppose the cascading of the filters is done by putting first the filter with frequency response H₂(jΩ)followed by the filter with frequency response H₁(jΩ). Does the response change? Explain.