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Mathematical Foundations

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Transmission of Information by Orthogonal Functions

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Abstract

A system {f(j,x)} of real and almost everywhere nonvanishing functions f(0,x), f(1,x),... is called orthogonal in the interval x0 ≦ x ≦ x1 if the following condition holds true:

$$\begin{gathered} \int\limits_{{x_0}}^{{x_1}} f \left( {j,x} \right)f\left( {k,x} \right)dx = {X_j}{\delta _{jk}} \hfill \\ {\delta _{jk}} = 1forj = k,{\delta _{jk}} = 0forj \ne k. \hfill \\ \end{gathered}$$
(1)

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Authors and Affiliations

  1. D-7501, Leopoldshafen, Western Germany

    Dr. Henning F. Harmuth (Consulting Engineer)

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Harmuth, H.F. (1969). Mathematical Foundations. In: Transmission of Information by Orthogonal Functions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13227-2_2

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  • DOI: https://doi.org/10.1007/978-3-662-13227-2_2

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  • Print ISBN: 978-3-662-13229-6

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