z-Transforms

  • Trevor J. Terrell
  • Lik-Kwan Shark
Chapter

Abstract

The Laplace transform plays an important role in the analysis of analogue signals or systems, since it uses a generalised complex frequency variable s = ± σ ± jω, with σ describing amplitude growth and decay of the sinusoidal signal having a radian frequency of ω,. However, complications arise in using the s-plane representation to analyse a sampled signal or sampled-data system due to their characteristic infinite number of complementary frequency spectra. Let us consider a sinusoidal signal cosω b t which, using Euler’s identity (e±jθ = cosθ ± jsinθ), can be expressed as
$$\cos \,\;{\omega _b}t = \frac{1}{2}\left( {{e^{j{\omega _b}t}} + {e^{ - j{\omega _b}t}}} \right)$$

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Copyright information

© Trevor J. Terrell and Lik-Kwan Shark 1996

Authors and Affiliations

  • Trevor J. Terrell
    • 1
  • Lik-Kwan Shark
    • 1
  1. 1.Department of Electrical and Electronic EngineeringUniversity of Central LancashirePrestonEngland

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