Reasons for using

orthogonal functions inside neural networks are stability and tracking performances improvement--which these functions could provide to a system [22].

Concerning these methods, they frequently use

orthogonal functions [1], in order to ease the calculations and to preserve the basis elements when dimensional expansions are necessary.

Some methods to do this are recursive algorithm [24], utilizing Gaussian input [24], Gradient-based search [25], Cross correlation method [26], Hilbert space reproduced kernel method [19, 20], expansion with

orthogonal functions [27-30] etc.

After reviewing the principles of

orthogonal functions and Walsh analysis, this graduate textbook explores the suitability of Walsh functions for the analysis of power electronic systems.

To remedy this, the projection of the field at the boundaries onto

orthogonal functions prior to reduction was proposed in [5,10].

Kozlov, On the complete systems of

orthogonal functions [in Russian], Mat.

EOF analysis is a useful technique for decomposition of a time series of geophysical data into temporal and spatial variability in terms of

orthogonal functions or statistical modes.

Continuous time dynamical systems; state estimation and optimal control with

orthogonal functions.

Fourier Series and

Orthogonal Functions, Dover Publications, Inc.

After an introduction to signals and systems, including properties of the delta function and some classical

orthogonal functions, the book provides examples and applications of numerous transforms.

Hardy, Notes on special systems of

orthogonal functions, IV: The

orthogonal functions of Whittaker's cardinal series, Proc.

DAVIS, An application of doubly

orthogonal functions to a problem of approximation in two regions, Trans.