Fourier Transforms of Stable Signals

Pierre Brémaud ()
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Pierre Brémaud: École Polytechnique Fédérale de Lausanne

Chapter A1 in Mathematical Principles of Signal Processing, 2002, pp 7-22 from Springer

Abstract: Abstract This first chapter gives the definition and elementary properties of the Fourier transform of integrable functions, which constitute the specific calculus mentioned in the introduction. Besides linearity, the toolbox of this calculus contains the differentiation rule and the convolution—multiplication rule. The general problem of recovering a function from its Fourier transform then receives a partial answer that will be completed by the results on pointwise convergence of Chapter A3.

Keywords: Inversion Formula; Rectangular Pulse; Pointwise Convergence; Gaussian Pulse; Stable Signal (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4757-3669-4_1

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