Abstract
The z-transform is very useful in the discrete-time world and plays an important role in system design and analysis. The Fourier transform of a sequence is obtained by evaluating the z-transform on the unit circle which has unit radius centered at z = 0. This chapter provides the definition of the z-transform, demonstrates some examples of sequences and their z-transforms, and points out that a z-transform should be defined with the region of convergence on the z-plane. The chapter also discusses the regions of convergence of four classes of sequences. The methods for finding the inverse z-transform by contour integral and other practical methods are also discussed and typical time is presented by sequences and their corresponding z-transforms. Finally, the chapter describes the properties of z-transforms, the relationship between the convolution sum of two sequences and the z-transform, and Parseval's equation.
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