The following three things are known about a signal x[n] with z-transform X(z):

(i) x[n] is real valued and minimum phase,

(ii) x[n] is zero outside the interval 0 ≤ n ≤ 4,

(iii) X(z) has a zero at z = ½ ejπ/4 and a zero at z = ½ ej3π/4. Based on this information, answer the following questions:

(a) Is X(z) rational? Justify your answer.

(b) Sketch the complete pole-zero plot for X(z) and specify its ROC.

(c) if y[n] * x[n] = δ[n] and y[n] is right sided, sketch the pole-zero plot for Y(z) and specify its ROC.