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 ...

In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...

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 ...

The Fourier transform underpins so much of our technological lives, in most cases probably without our realising it. The ability to mathematically split a waveform into its frequency components and ...

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 ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

In the last twenty years there have been many connections discovered between fractal geometry and harmonic analysis. One such connection is a Fourier transform formula for the energy integral of a ...