Results 1 to 10 of about 539,528 (73)

Uncertainty Principles for the Fourier and the Short-Time Fourier Transforms [PDF]

J. Math. Phys. 62(11): Paper No. 113501, 9 pp. (2021), 2020
The aim of this paper is to establish a few uncertainty principles for the Fourier and the short-time Fourier transforms. Also, we discuss an analogue of Donoho--Stark uncertainty principle and provide some estimates for the size of the essential support of the short-time Fourier transform.
arxiv   +1 more source

Circular Convolution and Product Theorem for Affine Discrete Fractional Fourier Transform [PDF]

arXiv, 2020
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of the discrete fractional Fourier transform, its applications in digital communications have been elusive.
arxiv  

A note on the Vilenkin-Fourier coefficients [PDF]

, 2014
The main aim of this paper is to find the estimation for Vilenkin-Fourier coefficients.
arxiv   +1 more source

On Fourier re-expansions [PDF]

arXiv, 2012
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
arxiv  

(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms [PDF]

, 2007
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on corresponding fundamental domains satisfying certain boundary conditions.
arxiv   +1 more source

Uniqueness sets for Fourier series [PDF]

arXiv, 2014
The paper discusses some uniqueness sets for Fourier series.
arxiv  

Lacunary Fourier and Walsh-Fourier series near L^1 [PDF]

, 2013
We prove that, for functions in the Orlicz class LloglogLloglogloglogL, lacunary subsequences of the Fourier and the Walsh-Fourier series converge almost everywhere. Our integrability condition is less stringent than the homologous assumption in the almost everywhere convergence theorems of Lie (Fourier case) and Do-Lacey (Walsh-Fourier case), where ...
arxiv   +1 more source

Fourier transform and related integral transforms in superspace [PDF]

, 2008
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach ...
arxiv   +1 more source

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform [PDF]

arXiv, 2015
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication.
arxiv  

Illuminating Fourier Series with Audacity [PDF]

arXiv, 2012
This paper briefly describes some simple techniques for illuminating Fourier series and Fourier analysis with the Audacity sound recording program. These techniques are easily applied in the classroom and help students move beyond formula roulette in their understanding of Fourier techniques.
arxiv