Temporal Pulse Compression Beyond the Fourier Transform Limit

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Original languageEnglish
Article number5971791
Pages (from-to)2173-2179
Journal / PublicationIEEE Transactions on Microwave Theory and Techniques
Issue number9
Online published4 Aug 2011
Publication statusPublished - Sep 2011
Externally publishedYes


It is a generally known that the Fourier transform limit forbids a function and its Fourier transform to both be sharply localized. Thus, this limit sets a lower bound to the degree to which a band-limited pulse can be temporally compressed. However, seemingly counterintuitive waveforms have been theoretically discovered, which, across finite time intervals, vary faster than their highest frequency components. While these so-called superoscillatory waveforms are very difficult to synthesize due to their high amplitude sidebands and high sensitivity, they open up the possibility toward arbitrarily compressing a temporal pulse, without hindrances from bandwidth limitations. In this paper, we report the design and realization of a class of superoscillatory electromagnetic waveforms for which the sideband amplitudes, and hence, the sensitivity can be regulated. We adapt Schelkunoff's method for superdirectivity to design such temporally compressed superoscillatory pulses, which we ultimately realize in an experiment, achieving pulse compression 47% improved beyond the Fourier transform limit.

Research Area(s)

  • Fourier transform limit, pulse compression, pulse shaping, superdirectivity