Authors: Milovanović, Miloš 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The Measurement Problem in Statistical Signal Processing
Journal: Mathematics
Volume: 11
Issue: 22
First page: 4623
Issue Date: 2023
Rank: ~M21a
ISSN: 2227-7390
DOI: 10.3390/math11224623
Abstract: 
Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for their claim is the insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is an adequate framework to elaborate the measurement problem. It considers signals to be stochastic processes, regardless of whether they correspond to variables or distribution densities. Signal processing that utilizes statistical properties to perform tasks is statistical signal processing. The hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has been generalized to an open system by the use of duality in frame theory.
Keywords: experimental mathematics | general measurement | time operator | frame wavelets | optimal decomposition
Publisher: MDPI

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