Characterization of the range of the Hilbert transform for bounded bandlimited signals and applications

Holger Boche, Ullrich J. Monich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Recently, a new constructive formula for the calculation of the Hilbert transform of bounded bandlimited signals was found. In this paper we use that formula to analyze the properties of the Hilbert transform. We further present a Fefferman-Stein-type decomposition theorem for bandlimited signals in BMO(ℝ), i.e., bandlimited signals of bounded mean oscillation. Based on this decomposition we characterize the range of the Hilbert transform and derive properties of general bandlimited signals in BMO(ℝ). We show the boundedness of bandpass signals in BMO(ℝ) and the boundedness of the derivative of bandlimited signals in BMO(ℝ). We further find the maximum growth of the Hilbert transform of bounded bandlimited signals.

Original languageEnglish
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages5388-5391
Number of pages4
DOIs
StatePublished - 18 Oct 2013
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: 26 May 201331 May 2013

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
Country/TerritoryCanada
CityVancouver, BC
Period26/05/1331/05/13

Keywords

  • Hilbert transform
  • bandlimited signal
  • bandpass signal
  • bounded mean oscillation
  • growth behavior

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