Related papers: Empirical Fourier Decomposition: An Accurate Adapt…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series…
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…
In precision frequency transfer systems, stringent requirements are imposed on the phase stability of transmitted signals. Throughout the transmission process, the inherent challenges of long-haul signal propagation inevitably introduce…
We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on…
Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies. These methods utilize Fourier transformations to shift signals…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
A univariate time series with high variability can pose a challenge even to Deep Neural Network (DNN). To overcome this, a univariate time series is decomposed into simpler constituent series, whose sum equals the original series. As…
Empirical Mode Decomposition is an adaptive and local tool that extracts underlying analytical components of a non-linear and non-stationary process, in turn, is the basis of Hilbert Huang transform, however, there are problems such as…
This paper proposes a novel approach for heartbeat classification from single-lead electrocardiogram (ECG) signals based on the novel adaptive Fourier decomposition (AFD). AFD is a recently developed signal processing tool that provides…
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…
Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…
Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust…
Finite-difference time-domain (FDTD) is an effective algorithm for resolving Maxwell equations directly in time domain. Although FDTD has obtained sufficient development, there still exists some improvement space for it, such as…
EEG emotion recognition faces significant hurdles due to noise interference, signal nonstationarity, and the inherent complexity of brain activity which make accurately emotion classification. In this study, we present the Fourier Adjacency…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…