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Measuremnt Problem in Statistical Signal Processing
Version 1
: Received: 18 October 2023 / Approved: 19 October 2023 / Online: 19 October 2023 (07:02:10 CEST)
A peer-reviewed article of this Preprint also exists.
Milovanović, M. The Measurement Problem in Statistical Signal Processing. Mathematics 2023, 11, 4623. Milovanović, M. The Measurement Problem in Statistical Signal Processing. Mathematics 2023, 11, 4623.
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 his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.
Keywords
experimental mathematics; general measurement; time operator; frame wavelets; optimal decomposition.
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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