Related papers: Time-Frequency Analysis of Fourier Integral Operat…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
Next-generation multiple-input multiple-output (MIMO) systems, characterized by extremely large-scale arrays, holographic surfaces, three-dimensional architectures, and flexible antennas, are poised to deliver unprecedented data rates,…
Nonstationary time series forecasting suffers from the distribution shift issue due to the different distributions that produce the training and test data. Existing methods attempt to alleviate the dependence by, e.g., removing low-order…
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
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…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
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…
Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…
The integration of operator kernels with the Wigner distribution, first conceptualized by E. Wigner in 1932 and later extended by L. Cohen and others, has opened new avenues in time-frequency analysis and operator calculus. Despite…
In this paper, we obtain an isometry between the Fock-Sobolev space and the Gauss-Sobolev space. As an application, we use multipliers on the Gauss-Sobolev space to characterize the boundedness of an integral operator on the Fock-Sobolev…
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the…