Finite Fourier Series and Cyclotomy

Determination of a jump by Fourier and Fourier-Chebyshev series

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Fourier series of finite products of Bernoulli and Genocchi functions

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

Finite Fourier Series and Ovals in PG(2, 2)

We propose the use of finite Fourier series as an alternative means of representing ovals in projective planes of even order. As an example to illustrate the method’s potential, we show that the set {w +w +w : 0 ≤ j ≤ 2} ⊂ GF(2) forms an oval if w is a primitive (2 +1) root of unity in GF(2) and GF(2) is viewed as an affine plane over GF(2). For the verification, we only need some elementary “t...

Cyclotomy and Trinomial Equations in a Finite Field.

Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...