Related papers: A Characterization of Metaplectic Time-Frequency R…
Periodically driven (Floquet) crystals are described by their quasi-energy spectrum. Their topological properties are characterized by invariants attached to the gaps of this spectrum. In this article, we define such invariants in all space…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are…
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one…
In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital…
We provide square-root n consistency results regarding estimation of the spectral representation of covariance operators of Hilbertian time series, in a setting with imperfect measurements. This is a generalization of the method developed…
General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the…
In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general phase space geometries obtained by diffeomorphic deformations…
This paper introduces a general technique for inter-mapping the complex spatial frequency (or propagation constant) $\gamma=\alpha+j\beta$ and the temporal frequency $\omega = \omega_\text{r}+j\omega_\text{i}$ of an arbitrary…
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…
It is common knowledge that the Fourier transform enjoys the convolution property, i.e., it turns convolution in the time domain into multiplication in the frequency domain. It is probably less known that this property characterizes the…
We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time…
We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at…
Time-frequency representations such as the spectrogram are commonly used to analyze signals having a time-varying distribution of spectral energy, but the spectrogram is constrained by an unfortunate tradeoff between resolution in time and…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…