The Measurement Problem in Statistical Signal Processing

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.