Temporal Pulse Compression Beyond the Fourier Transform Limit

• Published in: IEEE transactions on microwave theory and techniques Vol. 59; no. 9; pp. 2173 - 2179
• Main Authors: Wong, A. M. H., Eleftheriades, G. V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplitude modulation; Amplitudes; Antennas; Applied sciences; Bandwidth; Chebyshev approximation; Compressed; Compressing; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fourier transform limit; Fourier transforms; Information, signal and communications theory; Oscillators; Pulse compression; pulse shaping; Sensitivity; Sidebands; Signal and communications theory; Signal, noise; Studies; superdirectivity; Telecommunications and information theory; Temporal logic; Waveforms; Fourier transform limit; Lower bound; Signal compression; Fourier transformation; Electromagnetism; High sensitivity; Pulse shaping; Time interval; Localization; Sideband; Pulse compression; superdirectivity
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2011.2160961

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.