Journal of Fourier Analysis and Applications

, Volume 20, Issue 6, pp 1212–1233

Phaseless Signal Recovery in Infinite Dimensional Spaces Using Structured Modulations

Article

DOI: 10.1007/s00041-014-9352-3

Cite this article as:
Pohl, V., Yang, F. & Boche, H. J Fourier Anal Appl (2014) 20: 1212. doi:10.1007/s00041-014-9352-3

Abstract

This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex exponentials. Sufficient conditions are given such that almost every signal with compact support can be reconstructed up to a unimodular constant using only its magnitude samples in the frequency domain. Finally it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time-limited signal.

Keywords

Bernstein spaces Interpolation Phase retrieval Sampling  Signal reconstruction 

Mathematics Subject Classification

Primary 30D10 94A20 Secondary 42C15 94A12 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Lehrstuhl für Theoretische InformationstechnikTechnische Universität MünchenMünchenGermany
  2. 2.Department of Electrical Engineering and Computer ScienceUniversity of California-BerkeleyBerkeleyUSA

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