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Transmission of Information by Orthogonal Functions pp 10–89Cite as

Mathematical Foundations

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Abstract

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

$$\int\limits_{\mathop x\nolimits_0 }^{\mathop x\nolimits_1 } {f(j,x)f(k,x)dx = \mathop X\nolimits_j \mathop \delta \nolimits_{jk} } $$
((1))

δ jk = 1 for j = k, δ jk = 0 for j ≠ k

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  1. Department of Electrical Engineering, The Catholic University of America, Washington D.C., USA

    Dr. Henning F. Harmuth (Consulting Engineer and Adjunct Associate Professor)

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  1. Dr. Henning F. Harmuth
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Harmuth, H.F. (1972). Mathematical Foundations. In: Transmission of Information by Orthogonal Functions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61974-8_2

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