Question

Consider the cascade of two filters with frequency responses H 1 ( j Ω )   =   j Ω...

Consider the cascade of two filters with frequency responses

H 1 ( j Ω )   =   j Ω

H 2 ( j Ω )   =   1 e^{ - j Ω}

(1) Indicate what each of the filters does.

(2) Suppose that the input to the cascade is

x ( t )   =   p ( t )   cos ( πt / 2 ) ,  w h e r e   p ( t )   =   u ( t + 1 ) - u ( t - 1 ).

Find the output y(t) of the filter.

(3) Suppose we cascade the above filter by putting first H 2 followed by H1. Does the response change? Explain.

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