11,623 research outputs found
Time-frequency methods for coherent spectroscopy
Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed
Mixed-state localization operators: Cohen's class and trace class operators
We study mixed-state localization operators from the perspective of Werner's
operator convolutions which allows us to extend known results from the rank-one
case to trace class operators. The idea of localizing a signal to a domain in
phase space is approached from various directions such as bounds on the
spreading function, probability densities associated to mixed-state
localization operators, positive operator valued measures, positive
correspondence rules and variants of Tauberian theorems for operator
translates. Our results include a rigorous treatment of multiwindow-STFT
filters and a characterization of mixed-state localization operators as
positive correspondence rules. Furthermore, we provide a description of the
Cohen class in terms of Werner's convolution of operators and deduce
consequences on positive Cohen class distributions, an uncertainty principle,
uniqueness and phase retrieval for general elements of Cohen's class.Comment: We call generalized localization operators now mixed-state
localization operators. In addition to a change of title and other parts
involving generalized localization operators. We did a major revision of the
manuscript incorporating suggestions by reviewer
Cohen class of time-frequency representations and operators: boundedness and uncertainty principles
This paper presents a proof of an uncertainty principle of Donoho-Stark type
involving -concentration of localization operators. More general
operators associated with time-frequency representations in the Cohen class are
then considered. For these operators, which include all usual quantizations, we
prove a boundedness result in the functional setting and a form of
uncertainty principle analogous to that for localization operators.Comment: 21 pages, 1 figur
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