A linear time-invariant filter is described by the difference equation(a) Obtain an expres...

A linear time-invariant filter is described by the difference equation

(a) Obtain an expression for the frequency response of this system, and, using the fact that (1 − a)3 = l − 3a+3a2−a3, show that  can be expressed in the form

(b) Sketch the frequency response (magnitude and phase) as a function of frequency.

(c) What is the output if the input is x[n] = 10 + 4cos(0.5πn + π/4)?

(d) What is the output if the input is x[n] = δ[n]?

(e) Use superposition to find the output when x[n] = 10 + 4cos(0.5πn+ π/4) + 5δ[n − 3].