Yield-optimized superoscillations

Eytan Katzav, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

Abstract

Superoscillating signals are band-limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that an overwhelming proportion of the energy goes into that part of the signal, which is not superoscillating. In the present paper, we consider the problem of optimization of such signals. The optimization that we describe here is that of the superoscillation yield, the ratio of the energy in the superoscillations to the total energy of the signal, given the range and frequency of the superoscillations. The constrained optimization leads to a generalized eigenvalue problem, which is solved numerically. It is noteworthy that it is possible to increase further the superoscillation yield at the cost of slightly deforming the oscillatory part of the signal, while keeping the average frequency. We show, how this can be done gradually, which enables a tradeoff between the distortion and the yield. We show how to apply this approach to nontrivial domains, and explain how to generalize this to higher dimensions.

Original languageEnglish
Article number6497697
Pages (from-to)3113-3118
Number of pages6
JournalIEEE Transactions on Signal Processing
Volume61
Issue number12
DOIs
StatePublished - 2013

Keywords

  • Eigenvalues and eigenfunctions
  • quantum theory
  • supergain
  • superoscillations
  • superresolution
  • time-frequency analysis

Fingerprint

Dive into the research topics of 'Yield-optimized superoscillations'. Together they form a unique fingerprint.

Cite this