Related papers: Discrete Fourier Transform Approximations Based on…
In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as…
We study two discretisations of the nonlinear Fourier transform of AKNS-ZS type, ${\cal F}^E$ and ${\cal F}^D$. Transformation ${\cal F}^D$ is suitable for studying the distributions of the form $u = \sum_{n = 1}^N u_n \, \delta_{x_n}$,…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
We present a new fast approximate algorithm for Tukey (halfspace) depth level sets and its implementation-ABCDepth. Given a $d$-dimensional data set for any $d\geq 1$, the algorithm is based on a representation of level sets as…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
We present an algorithm that computes Friedl and L\"uck's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonn\'e determinant. The algorithm…
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from $n$ nonuniform points to $m$ nonuniform frequencies in $O((m+n)\log\min(n,m))$ operations. Our approach combines local and asymptotic Bessel…
We present a novel algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size N is a power of two. A direct method for calculation of the discrete fractional Hadamard transform requires $N^2$…
A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible…
This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
We introduce a novel algorithm that converges to level-set convex viscosity solutions of high-dimensional Hamilton-Jacobi equations. The algorithm is applicable to a broad class of curvature motion PDEs, as well as a recently developed…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
We give the first differentially private algorithms that estimate a variety of geometric features of points in the Euclidean space, such as diameter, width, volume of convex hull, min-bounding box, min-enclosing ball etc. Our work relies…
The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to calculate numerically single-side Fourier transforms of arbitrary autocorrelation functions from molecular simulations. However, the…