Uncertainty Relations and Time-Frequency Distributions for Unsharp Observables

This paper deals with a new framework in analyzing the formal mathematical correspondence between quantum mechanics and time-frequency representations of a signal. It is also shown that joint time-frequency distributions have a close link with Heisenberg uncertainty relations if the observables are taken as fuzzy entities. This result contradicts the arguments of Cohen [IEEE Proc. 77(7):941 (1989)] regarding the time-frequency distributions and the uncertainty relation. It is postulated that these mechanisms will be of crucial importance in highly fragmented computation structures, such as neural networks, as they may exhibit a strong mutual interaction between data and operator.

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