Related papers: Recall Gabor Communication Theory and Joint Time-F…
We propose the application of graphical convolution to the analysis of the resonance phenomenon. This time-domain approach encompasses both the finally attained periodic oscillations and the initial transient period. It also provides…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
This paper addresses the problem of efficiently jointly representing a non-stationary multicomponent signal in time and frequency. We introduce a novel enhancement of the time-reassigned synchrosqueezing method designed to compute sharpened…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to…
In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) one year observation time and (ii) arbitrary observation time, for arbitrary location of detector and source taking into…
Hundreds of applications utilize frequency response characterization of a system. Identification of frequency response requires long experimentation time, use of transformation techniques and other difficulties associated with isolating the…
Recent interest in the "memory effect" prompted us to revisit the relation of gravitational aves and oscillators. 50 years ago Niederer [1] found that an isotropic harmonic oscillator with a constant frequency can be mapped onto a free…
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study…
Not only motivated by the fact that the publication of the GAFT first appeared 60 years ago in print we reconstruct its history and so show that it is no exaggeration to claim that it has appeared already 75 years ago!
Recently it has been shown that the intensity time-bandwidth product of optical signals can be engineered to match that of the data acquisition instrument. In particular, it is possible to slow down an ultrafast signal, resulting in…
This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely the classically-equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by…
We develop a framework to track the structure of temporal networks with a signal processing approach. The method is based on the duality between networks and signals using a multidimensional scaling technique. This enables a study of the…
This article develops a general detection theory for speech analysis based on time-varying autoregressive models, which themselves generalize the classical linear predictive speech analysis framework. This theory leads to a computationally…
Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…
The characterization of non-stationary signals requires joint time and frequency information. However, time (t) and frequency (omega) being non-commuting variables there cannot be a joint probability density in the (t,omega) plane and the…
We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…
Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…