1.

Z transform reduces to discrete time fourier transform when the magnitude of the transform z is

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The Z transform is a generalization of the Discrete-Time Fourier Transform. It is used because the DTFT does not converge/exist for many important signals, and yet does for the z-transform. It is also used because it is notationally cleaner than the DTFT. In contrast to the DTFT, INSTEAD of using COMPLEX exponentials of the form eiωn, with purely imaginary parameters, the Z transform uses the more general, zn, where z is complex. The Z-transform THUS allows one to bring in the power of complex variable theory into DIGITAL Signal Processing.



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