Let $x (n)$ be a discrete sequence.

Part 1: DTFT and $Z T$

By definition of $Z-$transform, $X(z)=Z\{x[n]\}=\sum_{n=-\infty}^{\infty} x[n] \cdot z^{-n}$ and

By definition of Discrete Time Fourier transform, $X(\omega)=D T F T\{x[n]\}=\sum_{n=-\infty}^{\infty} x[n] \cdot e^{-j \omega n}$

It is found that, $X(z)=D T F T\left\{x[n] r^{-n}\right\}$

If $X(z)$ is …