| Issue |
EAS Publications Series
Volume 78-79, 2016
Mathematical Tools for Instrumentation & Signal Processing in Astronomy
|
|
|---|---|---|
| Page(s) | 99 - 126 | |
| Section | Mathematical Concepts, Methods and Tools | |
| DOI | https://doi.org/10.1051/eas/1678006 | |
| Published online | 02 September 2016 | |
Mathematical Tools for Instrumentation & Signal Processing in Astronomy
D. Mary, R. Flamary, C. Theys and C. Aime (eds)
EAS Publications Series, 78–79 (2016) 99-126
D. Mary, R. Flamary, C. Theys and C. Aime (eds)
EAS Publications Series, 78–79 (2016) 99-126
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
e-mail: aristidi@unice.fr
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.
© EAS, EDP Sciences, 2016