When last we saw [xoreaxeax], he had built a lens-less optical microscope that deduced the structure of a sample by recording ...

Fourier analysis provides a powerful framework for decomposing functions into sums or integrals of sinusoidal components, thereby enabling the study of frequency content in signals. In tandem, ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

Let f(u) be the Fourier-Stieltjes transform of a real or complex-valued function F(α) of bounded variation on (— ∞, ∞). It is shown that if f(u) belongs to L2 on an interval of infinite range, then ...

Every non-zero complex homomorphism of the almost periodic functions on an abelian group is induced by the Fourier transform. A Plancherel formula for almost periodic functions and a necessary ...

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 ...

Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous ...

When it comes to mathematics, the average person can probably get through most of life well enough with just basic algebra. Some simple statistical concepts would be helpful, and a little calculus ...

In less than 100 seconds, Carola-Bibiane Schönlieb of the University of Cambridge in the UK provides a basic definition of a Fourier transform. She explains how this mathematical tool was introduced ...