Adaptive Fourier Decomposition and Rational Approximation Techniques represent a significant evolution in the analysis and reconstruction of signals and functions. These methods extend classical ...

From the Maclaurin expansion of a function f̄(p) of the Laplace transform operator p, rational function approximations to f̄(p) are generated by means of a new nonlinear sequence to sequence ...

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, ...

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 ...

Arithmetic dynamics is an interdisciplinary field that investigates the behaviour of dynamical systems defined by rational maps on algebraic varieties, often over number fields. At its core, the ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...