A non-periodic random process cannot have unrelated random Fourier coefficients of the Fourier series representation, but the relationship can be used with a number of mutually

orthogonal function [[phi].

10) and (11) will cause an underestimation of the variances of the plane parameters fitted with the

orthogonal function for large AOI.

The book brings together ideas from classical

orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory.

Kozlov, On the complete systems of orthogonal functions [in Russian], Mat.

Paley, A remarkable set of orthogonal functions, Proc.

Continuous time dynamical systems; state estimation and optimal control with

orthogonal functions.

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.

He starts with the basic principles of electromagnetic theory, then moves to analytical methods and

orthogonal functions, Green's functions, computer integration and conformal mapping, Fourier transform methods, computational methods, method of finite differences, finite difference time domain analysis, and variational methods.

k](r))} is no longer a set of

orthogonal functions.

In this way one obtains one or two sets of

orthogonal functions, which are expressed in terms of a dual set of q-orthogonal polynomials (which corresponds to the indeterminate moment problem).