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Squdel Function: Square Wave Approximation Without Ringing

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Abstract

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.

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Authors and Affiliations

  1. Lab. de Óptica Cuántica, Depto. de Física, Universidad A. Metropolitana - Iztapalapa, Ap. postal 55-534, 09340, Mexico, D.F., Mexico

    M. Fernández-Guasti

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  1. M. Fernández-Guasti
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Correspondence to M. Fernández-Guasti.

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Fernández-Guasti, M. Squdel Function: Square Wave Approximation Without Ringing. Circuits Syst Signal Process 38, 764–773 (2019). https://doi.org/10.1007/s00034-018-0883-8

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  • DOI: https://doi.org/10.1007/s00034-018-0883-8

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