Related papers: A rational approximation of the Fourier transform …
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
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…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
A recent generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted $q$-Fourier transform. A representation formula for the…
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of…