Section-wise piecewise-linear functions: Canonical representation, properties, and applications
1977; Institute of Electrical and Electronics Engineers; Volume: 65; Issue: 6 Linguagem: Inglês
10.1109/proc.1977.10589
ISSN1558-2256
Autores Tópico(s)Digital Filter Design and Implementation
ResumoThis paper presents a new closed form analytical formula for representing n-dimensional surfaces and scalar functions of n variables which are piecewise-linear over each cross section obtained by freezing any combination of n - 1 of the n coordinates. This new section-wise piecewise-linear representation can be easily programmed with efficient computer storage. It is a global representation in the sense that a single formula is used to compute for f(x 1 ,x 2 ,...,x n ) for all values of (x 1 , x 2 ,...., x n ). Since this representation is expressed in closed analytic form, it allows standard mathematical operations and manipulations to be carried out in theorectical studies, In particular, it led to the possibility of deriving explicit closed form expressions for system parameters and design formulas. Examples are given which illustrate the potential applications of this representation in the modeling and analysis of nonlinear devices, circuits and systems.
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