Titel
On Foundational Discretization Barriers in STFT Phase Retrieval
Abstract
We prove that there exists no window function g∈L2(R) and no lattice L⊂R2 such that every f∈L2(R) is determined up to a global phase by spectrogram samples |Vgf(L)| where Vgf denotes the short-time Fourier transform of f with respect to g. Consequently, the forward operator f↦|Vgf(L)| mapping a square-integrable function to its spectrogram samples on a lattice is never injective on the quotient space L2(R)/~ with f∼h identifying two functions which agree up to a multiplicative constant of modulus one. We will further elaborate this result and point out that under mild conditions on the lattice L, functions which produce identical spectrogram samples but do not agree up to a unimodular constant can be chosen to be real-valued. The derived results highlight that in the discretization of the STFT phase retrieval problem from lattice measurements, a prior restriction of the underlying signal space to a proper subspace of L2(R) is inevitable.
Stichwort
Phase retrievalTime–frequency analysisShort-time Fourier transformLatticesSamplingSignal reconstruction
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
phaidra.univie.ac.at/o:1630995
Erschienen in
Titel
Journal of Fourier Analysis and Applications
Band
28
Ausgabe
2
ISSN
1069-5869
Erscheinungsdatum
2022
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2022
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2022
Universität Wien | Universitätsring 1 | 1010 Wien | T
+43-1-4277-0