Related papers: Instantaneous frequency and wave shape functions (…
In this paper, we develop a general method to estimate the instantaneous frequencies of the modes making up a multicomponent signal when the former exhibit interference in the time-frequency plane. In particular, studying the representation…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
Wavefunction collapse is a puzzling aspect of quantum mechanics. Designing a test to confirm the instantaneousness of collapse has turned out to be challenging, especially for collapse in configuration space. We propose a test using two…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending…
We study a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a configuration that can mimic…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…
We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of…
In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…
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…
We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…
The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of "Intrinsic Modes", supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its…
This text describes a generalization of the analytic signal (Gabor, 1946) approach for the definition of instantaneous amplitude and phase to the case of multivariate signals. It was originally written as an appendix for another paper,…