相关论文: Breaking the Limits -- Redefining the Instantaneou…

Bayesian statistical inference is a powerful tool for model-data comparisons and extractions of physical parameters that are often unknown functions of system variables. Existing Bayesian analyses often rely on explicit parametrizations of…

The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory…

Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representations are garbled when approaching the boundaries of the TF…

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the…

The Equivalent Effect Function (EEF) is defined as having the identical integral values on the control points of the original time series data; the EEF can be obtained from the derivative of the spline function passing through the integral…

We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals. It avoids several…

So far, problems of intermittent fault (IF) detection and detectability have not been fully investigated in the multivariate statistics framework. The characteristics of IFs are small magnitudes and short durations, and consequently…

This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related…

The origin of the "theoretical limit of time-frequency resolution of Fourier analysis" is from its numerical implementation, especially from an assumption of "Periodic Boundary Condition (PBC)," which was introduced a century ago. We…

Dynamic substructuring, especially the frequency-based variant (FBS) using frequency response functions (FRF), is gaining in popularity and importance, with countless successful applications, both numerically and experimentally. One…

We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited…

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,…

We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the {\it tendency} of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale…

The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on euclidean space, is incomplete for recovery, leading to the concept of moment indeterminateness. On the other hand, classical integral…

In this letter, based on the variational model, we propose a novel time-frequency post-processing technique to approximate the ideal time-frequency representation. Our method has the advantage of modularity, enabling "plug and play",…

The frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency independent…

The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…

Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…

Time-reflection is a uniform inversion of the temporal evolution of a signal, which arises when an abrupt change in the properties of the host material occurs uniformly in space. At such a time-interface, a portion of the input signal is…