Related papers: Asymptotically Steerable Finite Fourier-Bessel Tra…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…
Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…
We study the capability of the Fast Fourier Transform (FFT) to accelerate exact and approximate matrix multiplication without using Strassen-like divide-and-conquer. We present a simple exact algorithm running in $O(n^{2.89})$ time, which…
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…
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…
It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring…
Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier waveform for high mobility communications, is introduced here. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Accurate beam alignment is a critical challenge in XL-MIMO systems, especially in the near-field regime, where conventional far-field assumptions no longer hold. Although 2D grid-based codebooks in the polar domain are widely accepted for…
Data-dependent secondary transforms, which aim to decorrelate coefficients of a separable primary transform, can improve residual coding efficiency; however, their deployment is often constrained by computational complexity. Recent video…
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…
DFT is the numerical implementation of Fourier transform (FT), and it has many forms. Ordinary DFT (ODFT) and symmetric DFT (SDFT) are the two main forms of DFT. The most widely used DFT is ODFT, and the phase spectrum of this form is…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…
Object orientation provides a flexible framework for the implementation of the convolution of arbitrary distributions of real-valued random variables. We discuss an algorithm which is based on the discrete Fourier transformation (DFT) and…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
The discrete Hartley transform (DHT) is a useful tool for medical image coding. The three-dimensional DHT (3D DHT) can be employed to compress medical image data, such as magnetic resonance and X-ray angiography. However, the computation of…