4.2.6. Z-Transform and the Fourier Transform

Remember the Discrete Time Fourier Transform (DTFT):

\[\underline{X}(\Omega) = \sum_{n=-\infty}^{\infty} x[n] e^{-j\Omega n}\]

Comparing the above with the definition of the Z-transform we see that:

\[X(e^{j\Omega}) = \underline{X}(\Omega)\]

i.e. the Fourier transform can be found along the unit circle in the complex domain of the Z-transform.