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In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and…
A technique for timescale analysis of spectral lags performed directly in the time domain is developed. Simulation studies are made to compare the time domain technique with the Fourier frequency analysis for spectral time lags. The time…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we…
Motivated by analyzing complicated time series, nonlinear-type time-frequency analysis became an active research topic in the past decades. Those developed tools have been applied to various problems. In this article, we review those…
With the growing availability of multi-domain time series data, there is an increasing demand for general forecasting models pre-trained on multi-source datasets to support diverse downstream prediction scenarios. Existing time series…
The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem…
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative…
This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fourier basis functions, the nonlinear dynamical system is…
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…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed…
Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers. They often encode time series data in a black-box manner and rely on…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Diffusion probability models have shown significant promise in offline reinforcement learning by directly modeling trajectory sequences. However, existing approaches primarily focus on time-domain features while overlooking frequency-domain…
Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system…
Generalizability of deep learning models may be severely affected by the difference in the distributions of the train (source domain) and the test (target domain) sets, e.g., when the sets are produced by different hardware. As a…