Phase Retrieval from Sampled Gabor Transform Magnitudes: Counterexamples

被引：13

作者：

Alaifari, Rima ^{[1
]}

Wellershoff, Matthias ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Seminar Appl Math, HG G 58-3,Ramistr 101, CH-8092 Zurich, Switzerland

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2021年 / 28卷 / 01期

关键词：

Phase retrieval; Gabor transform; Sampling theory; lime-frequency analysis; UNIQUENESS;

D O I：

10.1007/s00041-021-09901-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered from such samples. In particular, we show that for any lattice, one can construct functions in L-2(R) which do not agree up to global phase but whose Gabor transform magnitudes sampled on the lattice agree. These functions have good concentration in both time and frequency and can be constructed to be real-valued for rectangular lattices.

引用

页数：8

共 6 条

[1] Uniqueness of STFT phase retrieval for bandlimited functions
Alaifari, Rima
Wellershoff, Matthias
[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2021, 50 : 34 - 48
[2] Grochenig K., 2001, FDN TIME FREQUENCY A, DOI [10.1007/978-1-4612-0003-1, DOI 10.1007/978-1-4612-0003-1]
[3] Grohs P., 2020, ARXIV PREPRINT ARXIV
[4] Grohs P., ARXIV PREPRINT ARXIV
[5] Uniqueness results in an extension of Pauli's phase retrieval problem
Jaming, Philippe
[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2014, 37 (03) : 413 - 441
[6] Phase retrieval and magnitude retrieval of entire functions
McDonald, JN
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2004, 10 (03) : 259 - 267

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