Circuits, Systems, and Signal Processing

, Volume 38, Issue 2, pp 764–773 | Cite as

Squdel Function: Square Wave Approximation Without Ringing

  • M. Fernández-GuastiEmail author


A function that is well suited to describe a square wave as well as a sequence of delta functions is presented. The squdel function has a closed rational form instead of a series approximation. Bandwidth limitations are readily incorporated in this function without producing undesirable ringing artifacts. The squdel function is infinitely differentiable and analytic for a squareness parameter as close as required to the square function provided that the limit is not taken. Even its Fourier series decomposition does not exhibit overshooting when truncated. Two-dimensional soft pixel structures are shown to be economically modeled with this function.


Wave synthesis Square wave Dirac comb Limited bandwidth Ringing Pixel shape 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lab. de Óptica Cuántica, Depto. de FísicaUniversidad A. Metropolitana - IztapalapaMexicoMexico

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