Question

The Z – Transform of a function is given by \(U(z) = \frac{z^3+6z^2+9z+3}{(z-1)^4}\). Find the Z-Transform of un+2.

(a) \(\frac{10z^3+3z^2+7z^1-1}{(z-1)^4} \)

(b) \(\frac{10z^4+3z^3+7z^2-z}{(z-1)^4} \)

(c) \(\frac{10z^4+4z^3+7z^2-2z}{(z-1)^4} \)

(d) \(\frac{10z^4+3z^3-4z}{(z-1)^4} \)

The question was posed to me during an online interview.

Question is from Linear Difference Equations and Z topic in section Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Correct answer is (b) \(\frac{10z^4+3z^3+7z^2-z}{(z-1)^4} \)

Explanation: First we have to find u0, which can be found by applying limits to U(z). Now shifting by 1 and then applying limits we get u1. Now using the second shift property, we find the Z-Transform of un+2.