A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...

In this paper, we study the quenched central limit theorem for the discrete Fourier transform. We show that the Fourier transform of a stationary ergodic process, suitable centered and normalized, ...

The classical Bochner-Schoenberg-Eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group G which arise as Fourier-Stieltjes transforms of elements ...

Fourier Restriction Theory investigates the conditions under which the Fourier transform of a function, when confined to a geometric surface such as a sphere, paraboloid or other manifold, remains ...

The representation of a periodic sound or waveform as a sum of Fourier components (i.e. pure sinusoidal waves). According to the Fourier theorem, periodic sound may be shown to consist of sine waves ...

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, ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...