Systems theory to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems. People have studied subjects like complexity, self-organization, connectionism and adaptive systems in the 1940s and 1950s. In fields like cybernetics, researchers such as Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster, examined complex systems mathematically. John von Neumann discovered cellular automata and self-reproducing systems, again with only pencil and paper. Aleksandr Lyapunov and Jules Henri Poincaré worked on the foundations of chaos theory without any computer
Wiener series by Norbert Wiener used in signal processing. Given a system with an input/output pair formula_1 where the input is white noise with zero mean value and power A, we can write the output of the system as sum of a series of Wiener G-functionals formula_2 In the following the expressions of the G-functionals up to the fifth order will be given: formula_3 formula_4 formula_5 formula_6 formula_7 formula_8 formula_9 formula_10 formula_11 Wiener series In mathematics, the Wiener series (or "Wiener G-functional expansion") originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to