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.

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

(c) Determine the output if the input signal is x[n] = 4 + cos(0.257πn – π/4).

(d) The signal x1[n] = (4 + cos(0.25πn – π/4)) u[n] is zero for n<0, so it "starts" at n = 0. If the input signal is x1[n] for which values of n will the corresponding output be equal to the output obtained in (c)?