question 4 and 5 please expressed as a rational function of z . Problem 4 For pr

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question 4 and 5 please

expressed as a rational function of z . Problem 4 For practical reasons, we focus primarily on z transforms that are rational functions of z.This does not mean that every signal has a z transform that is a rational function of 1 . Demonstrate this by finding aiclosed-form expression for the z transform of Hint: what is the Taylor series of e? Problem 5 (a) Express the running sum y(n)= ? x(k) as a convolution y(n)=h(n)*x(n) for some h(n) (b) Given X (z), what is Y(z)? here to search

Explanation / Answer

e x = 1 + x + x 2 2! + x 3 3! + x 4 4! + . . . so: e = 1 + 1 + 1 2! + 1 3! + 1 4! + . . . e (17x) = P? n=0 (17x) n n! = X? n=0 17nx n n! = X? n=0 x n n!

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