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Orthogonal Functions may be divided into two classes. The class of
continuous systems and the discontinuous class of piecewise
constant systems. Problems arise because continuous systems form an
unsatisfactory basis for the expansion of functions containing
discontinuities whilst piecewise constant systems insert artificial
discontinuities into all representations. Since these two classes
of functions would be unsuccessful in coping with functions that
possess both continuity and discontinuity we must look to General
Hybrid Orthogonal Functions (GHOF) which have been shown to be the
most appropriate in such situations. This book introduces the
system of GHOF, discusses its properties, develops an operational
algebra for the discretization of continuous dynamic systems on the
system of GHOF and illustrates its use as a flexible and powerful
framework of computational tools in a wide range of systems and
control.
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