Norbert Wiener the development of the digital theory. Wiener originated cybernetics, a formalization of the notion of feedback, with many implications for engineering, systems control, computer science, biology, philosophy, and the organization of society. Wiener's work with cybernetics influenced Gregory Bateson and Margaret Mead, and through them, anthropology, sociology, and education. A simple mathematical representation of Brownian motion, the Wiener equation, named after Wiener, assumes the current velocity of a fluid particle fluctuates randomly. For signal processing, the Wiener filter is a filter proposed by Wiener during the 1940s and published in 1942 as a classified document. Its purpose is to reduce
Wiener algebra functions on the unit circle. On the other hand an integration by parts, together with the Cauchy–Schwarz inequality and Parseval's formula, shows that More generally, for formula_8 (see ). proved that if has absolutely convergent Fourier series and is never zero, then its inverse also has an absolutely convergent Fourier series. Many other proofs have appeared since then, including an elementary one by . which is equivalent to Wiener's theorem. Wiener algebra In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by , is the space of absolutely convergent Fourier series. Here denotes the circle group. The