Mathematics and Signal Analysis

Mathematics and Signal Analysis

This course focuses on the main mathematical tools used in signal analysis. It is structured in three main chapters:  Complex analysis, Distribution theory, and Fourier analysis. A more detail syllabus is as follows:  

Complex analysis (7h)

Analytic functions, Holomorphic functions, Laurent series, singularities, contour integration, Cauchy theorem, Residue theorem, applications to the evaluation of real intégrals.

Distribution theory (7)

Test functions, regular distributions, singular distributions, examples and elementary properties: derivation, multiplication by a function, Fourier transform, representation of discontinuities, convolution, etc.

Fourier analysis (10)

Fourier series, Fourier transform, definition, examples, properties (scaling, derivation, convolution, etc). Application to the signal analysis: Gibbs phenomenon, tapering, sampling theorem, aliasing, filtering.