The frequency response of a linear time-invariant filter is given by the formula(a) Write...

The frequency response of a linear time-invariant filter is given by the formula

(a) Write the difference equation that gives the relation between the input x[n] and the output y[n].

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

(c) If the input is of the form , for what values of  will y[n] = 0 for all n?