Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

• Autorzy: Chen Lung-Hui

Identyfikatory

DOI

10.1515/jaa-2021-2052

• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss how to partially determine the Fourier transform F(z) = ¹ ∫ ₋₁ f(t)e^izt dt, z ∈ ℂ, given the data |F(z)| or arg F(z) for z ∈ ℝ. Initially, we assume [−1, 1] to be the convex hull of the suport of the signal f . We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F(z). Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness.We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform.We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Słowa kluczowe

EN

phase retrieval; magnitude retrieval; phaseless problem; inverse Fourier transform; band limited signal; Nevanlinna-Levin theorem

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 2
• Strony: 259--268
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Chen Lung-Hui

• General Education Center, Ming Chi University of Technology, New Taipei City, 24301, Taiwan

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)