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The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this non trivial dynamics is still not well understood, although recent…
Charge density wave (CDW) is a widely concerned emergent phenomenon in condensed matter physics. To establish a systematic understanding of CDW, we develop a diagrammatic self-consistent-field approach for cubic Holstein model employing…
Estimating closely spaced frequency components of a signal is a fundamental problem in statistical signal processing. In this letter, we introduce 1-D real-valued and complex-valued shifted window (Swin) transformers, referred to as…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
In this paper, we propose a new convolutional layer called Depthwise-STFT Separable layer that can serve as an alternative to the standard depthwise separable convolutional layer. The construction of the proposed layer is inspired by the…
The information regarding how the intergalactic medium is reionized by astrophysical sources is contained in the tomographic three-dimensional 21 cm images from the epoch of reionization. In Zhao et al. (2022a) ("Paper I"), we demonstrated…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
Several kinds of spin density wave (SDW) states with both quarter-filled band and dimerization are reexamined for a one-dimensional system with on-site, nearest-neighbor and next-nearest-neighbor repulsive interactions, which has been…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
Spatial and temporal delays in a wireless multi-antenna system, paired with an orthogonal frequency division multiplexing (OFDM) waveform, can be utilized to estimate the Angle of Arrival (AoA) and Time of Arrival (ToA) of scatterers in the…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
As Extremely large-scale array (XL-array) technology advances and carrier frequency rises, the near-field effects in communication are intensifying. In near-field conditions, channels exhibit a diffusion phenomenon in the angular domain,…
The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection…
In general, there is an inverse relation between the degree of localization of a wavefunction of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of…