Discontinuous functions represented by exact, closed, continuous parametric equations

Authors:
Enrique Chicurel-Uziel
Affiliations:
Instituto de Ingeniería, Universidad Nacional Autónoma de México, México, D. F., Mexico
Venue:
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Year:
2010

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Abstract

A simple procedure is proposed to represent a discontinuous function by continuous parametric equations without a significant change in the nature of the original function. Furthermore, this representation is exact and closed. As it is well known, series expansions of functions with discontinuities are plagued by spurious oscillations due to the Gibbs phenomenon. Since in the proposed parametric representation there are no discontinuities, no Gibbs phenomenon arises in its series expansion.