Consider a discrete-time LTI filter whose impulse response h[n] is nonzero only over fiv...

Consider a discrete-time LTI filter whose impulse response h[n] is nonzero only over five consecutive time samples; the filter’s frequency response is H(e^jω). Let signals x[n] and y[n] denote the filter’s input and output, respectively.

Moreover, you are given the following information about the filter:

ii) There exists a signal a[n] that has a real and even DTFT A(e^jω) given by

A(e ^{j ω} ) = H(e^jω) e^j2ω.

(iii) A(e^j0) = 8 , and A(e^jπ ) = 12 .

Completely specify the impulse response h[n], i.e., specify the impulse response at each time instant where it takes a nonzero value. Plot h[n], carefully and accurately labeling its salient features.