Question

If x(n)=a^n, then what is one sided z-transform of x(n+2)?

(a) \(\frac{z^{-2}}{1-az^{-1}}\) + a^-1z^-1 + a^-2

(b) \(\frac{z^{-2}}{1-az^{-1}}\) – a^-1z^-1 + a^-2

(c) \(\frac{z^2}{1-az^{-1}}\) + a z + z^2

(d) \(\frac{z^2}{1+az^{-1}}\) – z^2 – az

This question was posed to me during an interview for a job.

Asked question is from One Sided Z Transform in chapter Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right choice is (d) \(\frac{z^2}{1+az^{-1}}\) – z^2 – az

Explanation: We will apply the time advance theorem with the value of k=2.We obtain,

Z^+{x(n+2)}=z^2 X^+(z)-x(0)z^2-x(1)z

=>X1^+(z)=\(\frac{z^2}{1+az^{-1}}\) – z^2 – az.