The following system has input x[n] = 9 + 2cos(n/2) + 3cos(n) and output y[n]: 5y[n] + 3y[n − 1] + y[n − 2] = 7x[n] + 6x[n − 1] − x[n − 2] . Calculate: (a) the frequency response H(e j ), and (b) the output y[n].

a) H(e^jΩ) = ye^jΩ/xe^jΩ = (7+6e^-jΩ-e^-j2Ω)/(5+3e^-jΩ+e^-j2Ω)

b) y(n) = 12 + 4cos((πn)/2)

Step-by-step explanation:

the explanation of the answer step by step is shown in the attached image

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

m∠a is 90°

m∠b is 40°