Question

Find the Z-transform of δ(n+3).

(a) z

(b) z^2

(c) 1

(d) z^3

I have been asked this question in a job interview.

I want to ask this question from The Z-Transform topic in chapter Z-Transform and Digital Filtering of Signals and Systems

Answer 1

The correct answer is (d) z^3

For explanation: Given x(n) = δ(n+3)

We know that δ(n+3) = \(

\begin{cases}

1 &\text{\(n=-3\)} \\

0 &\text{otherwise} \\

\end{cases}\)

X(Z) = \(\sum\limits_{n=-\infty}^{\infty} x(n) z^{-n} = \sum\limits_{n=-\infty}^{\infty} δ(n+3) z^{-n}\) = z^3.