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On the Numerical Evaluation of Bandpass Prolates II

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Abstract

We provide a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable function on the real line to a finite interval, followed by frequency limiting to frequencies in an annular band. When the width of the annulus is small relative to the mean radius of the annulus the method is more accurate than one previously suggested by the authors.

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Acknowledgments

The authors would like to thank the anonymous referee for pointing out that the accuracy of our method for estimating the matrix exponential \(\mathrm{e}^{2\pi \mathrm{i}\Omega _0 T_N}\) should be checked against other methods for computing matrix exponentials.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308, Australia

    Jeffrey A. Hogan

  2. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003–8001, USA

    Joseph D. Lakey

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  1. Jeffrey A. Hogan
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  2. Joseph D. Lakey
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Correspondence to Joseph D. Lakey.

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Communicated by Hans G. Feichtinger.

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Hogan, J.A., Lakey, J.D. On the Numerical Evaluation of Bandpass Prolates II. J Fourier Anal Appl 23, 125–140 (2017). https://doi.org/10.1007/s00041-016-9465-y

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  • DOI: https://doi.org/10.1007/s00041-016-9465-y

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