This post covers topic of fourier representation of a function. Most signals are represented with a set of exponential functions, resulting in complex exponential functions. If these functions are ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

Abstract: The comb function is defined as equidistantly spaced impulses (i.e., an impulse train); it is well known that its Fourier transform also provides a comb function, and is used for a proof of ...

Abstract: In this paper, the discrete Fourier transform (DFT) of Boolean functions over the complex field is introduced and the locations of zero-valued Fourier spectrum are studied. Then a Fourier ...

FS=1000 #number of discrete values of t between BT and ET #the periodic complex-valued function f(t) with period equal to P f = lambda t: ((t % P) - P/2.) ** 2 + ((t % P) -P/2.) * 1j t_range = ...

Fourier Value Functions (FVF) are a framework for leverging Fourier-based techniques for value function approximation for use in policy learning. More preciesly, FVFs are SO(2)/SO(3)-equivariant ...

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic ...

The COS method was introduced in Fang & Oosterlee (2008) and then was applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) ...