Representation of Signals as Series of Orthogonal Functions

Laboratoire Lagrange, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Parc Valrose, 06108 Nice Cedex 2, France

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Abstract

This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for 2D signals. We show how physical conditions and/or geometry can guide the choice of the base of functions for the decomposition. The paper is illustrated with several numerical examples.