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Scaling properties of superoscillations and the extension to periodic signals

Tang, Eugene and Garg, Lovneesh and Kempf, Achim (2016) Scaling properties of superoscillations and the extension to periodic signals. Journal of Physics A: Mathematical and Theoretical, 49 (33). Art. No. 335202. ISSN 1751-8113. doi:10.1088/1751-8113/49/33/335202. https://resolver.caltech.edu/CaltechAUTHORS:20160729-105121641

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Abstract

Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more pronounced the desired superoscillatory behavior is to be, the more difficult it becomes to produce, or even only calculate, such highly fine-tuned wave forms in practice. Here, we investigate how this sensitivity to preparation errors scales for a method for constructing superoscillatory functions which is optimal in the sense that it minimizes the energetic expense. We thereby also arrive at very accurate approximations of functions which are so highly superoscillatory that they cannot be calculated numerically. We then investigate to what extent the scaling and sensitivity results for superoscillatory functions on the real line extend to the experimentally important case of superoscillatory functions that are periodic.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1088/1751-8113/49/33/335202DOIArticle
http://iopscience.iop.org/article/10.1088/1751-8113/49/33/335202/metaPublisherArticle
https://arxiv.org/abs/1512.00109arXivDiscussion Paper
Additional Information:© 2016 IOP Publishing Ltd. Received 16 December 2015, revised 4 April 2016; Accepted for publication 10 June 2016; Published 8 July 2016. AK, LG and ET acknowledge support from the Discovery, Engage, and USRA programmes of the National Science and Engineering Research Council of Canada (NSERC), respectively.
Funders:
Funding AgencyGrant Number
National Science and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Issue or Number:33
DOI:10.1088/1751-8113/49/33/335202
Record Number:CaltechAUTHORS:20160729-105121641
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160729-105121641
Official Citation:Eugene Tang et al 2016 J. Phys. A: Math. Theor. 49 335202
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69303
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 Jul 2016 19:02
Last Modified:11 Nov 2021 04:12

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