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
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).