Related papers: The inverse cyclotomic Discrete Fourier Transform …
We show that simple modifications to van der Hoeven's forward and inverse truncated Fourier transforms allow the algorithms to be performed in-place, and with only a linear overhead in complexity.
Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
A class theorem is presented and proved: the complex Fourier transforms of a certain class of exponential functions have all their zeros on the real line. A class of basis functions is first considered, and the class is then extended via…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…
It is shown that, given a representation of a quiver over a finite field, one can check in polynomial time whether it is absolutely indecomposable.
We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We develop a Galois descent approach to finite-field Fourier spectra over an arbitrary finite base field. Let $\mathbb K=\mathbb F_q$ and $\mathbb L=\mathbb F_{q^m}$. If a Fourier transform is applied to a $\mathbb K$-valued vector, then…
In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic…
We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus…