A new algorithm performs Fourier transforms using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing.

The linear canonical transform (LCT) is a versatile integral transform that generalises classical transforms such as the Fourier, fractional Fourier, and Fresnel transforms. By utilising four ...

Design linear discrete-time systems and filters and analyze their behavior. Represent continuous-time signals and linear systems in discrete time, so that such signals can be recovered in continuous ...

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, ...

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals. In an increasingly data-driven world, ...