In mathematics and signal
processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex
numbers, into a complex frequency-domain representation. It is like a discrete equivalent of the Laplace
transform. This similarity is explored in the theory of time scale calculus. The Z-transform was introduced, under
this name, by Ragazzini and Zadeh in 1952. The modified or advanced Z-transform was later developed by E. I. Jury,
and presented in his book Sampled-Data Control Systems (John Wiley & Sons 1958). The idea contained within the
Z-transform was previously known as the "generating function method".
- Wikipedia

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where C is a closed contour that includes z=0

Signal

z-Transform

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(convolution)

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