Define a discrete-time signal using the formula:


(a) Make a sketch of y[n] versus n, as a “stem” plot. Take the range of n to be 0 ≤ n ≤ 20.

(b) Design an IIR filter that will synthesize y[n]. Give your answer in the form of a difference equation with numerical values for the coefficients. Assume that the synthesis will be accomplished by using an impulse input to “start” the difference equation (which is at rest; i.e., has zero initial conditions).