Related papers: One or two frequencies? The Iterative Filtering an…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non-stationary and non-linear signals. Recently in [1] IF has been proved to be convergent for any $L^2$…
In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years,…
The Empirical Mode Decomposition (EMD) is a signal analysis method that separates multi-component signals into single oscillatory modes called intrinsic mode functions (IMFs), each of which can generally be associated to a physical meaning…
The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we…
This paper consists of two parts. First, the (undirected) Hamiltonian path problem is reduced to a signal filtering problem - number of Hamiltonian paths becomes amplitude at zero frequency for (a combination of) sinusoidal signal f(t) that…
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…
A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…
Many real-life signals, such as gravitational wave measurements, biomedical signals, or geophysical data, are strongly non-stationary but can be decomposed into mono-component signals that contain only one active frequency over time. This…
Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of…
In this paper, we introduce a sequential variational mode decomposition method to separate non-stationary mixed signals successively. This method is inspired by the variational method, and can precisely recover the original components one…
The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…