Representation of Signals as Series of Orthogonal Functions

E. Aristidi (1)

1 LAGRANGE - Joseph Louis LAGRANGE

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.

Domaines: Astrophysique [astro-ph]

E. Aristidi. Representation of Signals as Series of Orthogonal Functions. Mathematical Tools for Instrumentation & Signal Processing in Astronomy, Sep 2016, Nice, France. pp.99-126, ⟨10.1051/eas/1678006⟩. ⟨hal-02476488⟩