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An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of exponential expansion (de–Sitter space) or uniform acceleration (Rindler trajectories) or both, but the real cosmic expansion is non–exponential and real accelerations are non–uniform. Here we use the frequency–time Wigner function of vacuum correlations to define time–dependent spectra. We found excellent Planck spectra for a class of realistic cosmological models, but also strongly non–Planckian, negative Wigner functions for a standard scenario testable with laboratory analogues.

Abstract: A novel modelling scheme that can be used to estimate and track time-varying properties of nonstationary signals is investigated. This scheme is based on a class of time-varying AutoRegressive with an eXogenous input (TVARX) models where the associated time-varying parameters are represented by multi-wavelet basis functions. The orthogonal least square (OLS) algorithm is then applied to refine the model parameter estimates of the TVARX model. The main features of the multi-wavelet approach is that it enables smooth trends to be tracked but also to capture sharp changes in the time-varying process parameters. Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes. [Copyright &y& Elsevier]

The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke spacetimes are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time. [ABSTRACT FROM AUTHOR]

It has been well understood that a given signal can be represented in an infinite number of different ways. Different signal representations can be used for different applications. For example, signals obtained from most engineering applications are usually functions of time. But when studying or designing the system, we often like to study signals and systems in the frequency domain. Although the frequency content of the majority of signals in the real world evolves over time, the classical power spectrum does not reveal such important information. In order to overcome this problem, many alternatives, such as the Gabor (1946) expansion, wavelets, and time-dependent spectra, have been developed and widely studied. In contrast to the classical time and frequency analysis, we name these new techniques joint time-frequency analysis. We introduce the basic concepts and well-tested algorithms for joint time-frequency analysis. Analogous to the classical Fourier analysis, we roughly partition this article into two parts: the linear (e.g., short-time Fourier transform, Gabor expansion) and the quadratic transforms (e.g., Wigner-Ville (1932, 1948) distribution). Finally, we introduce the so-called model-based (or parametric) time-frequency analysis method [ABSTRACT FROM PUBLISHER]