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This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal formulation transforms into multiplication in Fourier space and…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling patterns, the system models typically involve non-uniform…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…
Bilinear time-frequency representations (TFRs) provide high-resolution time-varying frequency characteristics of nonstationary signals. However, they suffer from crossterms due to the bilinear nature. Existing crossterm-reduced TFRs focus…
The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k…
In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…
This paper proposes a multivariable extremum seeking scheme using Fast Fourier Transform (FFT) for a network of subsystems working towards optimizing the sum of their local objectives, where the overall objective is the only available…
This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here we consider the continuous…
This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version…
Many robotic exploration algorithms rely on graph structures for frontier-based exploration and dynamic path planning. However, these graphs grow rapidly, accumulating redundant information and impacting performance. We present a…
By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of…
While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…