Thursday, April 13, 2017

Finding Fourier transform of a discrete signal from its Z-transform


Is it possible to find the Fourier transform of a discrete signal if you know its $\mathcal{Z}$-transform of?



Answer



DTFT is the Z-transform at the unit circle. So if $z=re^{j\omega}$ then for DTFT $r = 1$.



i.e If you have the Z-transform of a signal then plug-in $e^{j\omega}$ for every $z$


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