Representation of signals as series of orthogonal functions. (arXiv:1811.07305v1 [astro-ph.IM])

Representation of signals as series of orthogonal functions. (arXiv:1811.07305v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Aristidi_E/0/1/0/all/0/1">Eric Aristidi</a>

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.

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.

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