2    z-Transform

Given a complete mathematical expression for a discrete time-domain signal, why transform it to another domain? The main reason for time–frequency transforms is that many mathematical reductions are much simpler in one domain than the other [1]. The z-transform in the digital domain is the counterpart to the Laplace transform in the analog domain. The z-transform is an extremely useful tool for analyzing the stability of digital sequences, designing stable digital filters, and relating digital signal processing operations to the equivalent mathematics in the analog domain. The Laplace transform provides a systematic method for solving analog systems described by differential equations. Both the z-transform and the Laplace ...

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