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

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 ...

Joseph Fourier was a French mathematician, born on 21 March 1768 in Auxerre, France. His name is closely associated with the Fourier series and Fourier transform, mathematical tools utilised in a wide ...

This is a preview. Log in through your library . Abstract We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideand-conquer algorithms (fast Fourier transforms, or FFTs ...

An optical imaging system generally consists of an illumination source and a light detection unit. For conventional imaging techniques, a scene is illuminated by a uniform light field and detected ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

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 ...