An LTI filter is described by the difference equation(a) What is the impulse response h[n]...

An LTI filter is described by the difference equation

(a) What is the impulse response h[n] of this system?

(b) Obtain an expression for the frequency response of this system.

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

(d) Suppose that the input is

for –∞>n>∞. Obtain an expression for the output in the form .

(e) Suppose that the input is

where u[n] is the unit-step sequence. For what values of n will the output y1[n] be equal to the output y[n] in (d)?