Spectral Representation of Deterministic Signals: Fourier Series and Transforms



In this chapter we will take a closer look at the spectral, or frequency-domain, representation of deterministic (nonrandom) signals which was already mentioned in Chap. 1. The tools introduced below, usually called Fourier, or harmonic, analysis will play a fundamental role later in our study of random signals. Almost all of the calculations will be conducted in the complex form. Compared with working in the real domain, the manipulation of formulas written in the complex form turns out to be simpler and all the tedium of remembering various trigonometric formulas is avoided. All of the results written in the complex form can be translated quickly into results for real trigonometric series expressed in terms of sines and cosines via the familiar de Moivre’s formula from Chap. 1, e jt = cos t = j sin t.


Fourier Series Spectral Representation Periodic Signal Fourier Expansion Complex Exponential 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and TechnologyCase Western Reserve UniversityClevelandUSA

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