Taking the [[z-transform]] equation and representing $z$ in polar coordinates ($z=r e^{j\omega}$): $ X(z) = \sum_{n = -\infty}^{+\infty} x(n) z^{-n} \xrightarrow[z = r e^{j\omega}]{} \; X(r e^{j\omega}) = \sum_{n = -\infty}^{+\infty} (x(n) r^{-n}) e^{-j\omega n} $ The [[discrete-time Fourier transform (DTFT)]] is the z-transform over the unit circle $|z|=r=1$: $ X(e^{j\omega}) = \sum_{n = -\infty}^{+\infty} x(n) e^{-j\omega n} $ ![[unitcirc.svg]]