Translations:Z-transform/51/en

by the substitution $Z=e^{-i\omega }$. The locus of $Z=e^{-i\omega }$ is the unit circle ${|}Z{|}=1$. As angular frequency increases from $\omega =-\pi$ through $\omega =0$ to $\omega =\pi$, the point $Z=e^{-i\omega }$ goes around the unit circle (in a clockwise direction) from Z = +1 through Z = +i to Z = -1. The Fourier transform represents the value of the Z-transform on the unit circle (Figure 1).