Norbert Wiener firing of anti-aircraft guns caused Wiener to investigate information theory independently of Claude Shannon and to invent the Wiener filter. (To him is due the now standard practice of modeling an information source as a random process—in other words, as a variety of noise.) His anti-aircraft work eventually led him to formulate cybernetics. After the war, his fame helped MIT to recruit a research team in cognitive science, composed of researchers in neuropsychology and the mathematics and biophysics of the nervous system, including Warren Sturgis McCulloch and Walter Pitts. These men later made pioneering contributions to computer science and artificial
Wiener filter criterion of the latter does not rely on cross-correlations or auto-correlations. Its solution converges to the Wiener filter solution. For complex signals, the derivation of the complex Wiener filter is performed by minimizing formula_55 =formula_56. This involves computing partial derivatives with respect to both the real and imaginary parts of formula_32, and requiring them both to be zero. The resulting Wiener-Hopf equations are: which can be rewritten in matrix form: Note here that:formula_60 The Wiener coefficient vector is then computed as:formula_61 The Wiener filter has a variety of applications in signal processing, image processing, control systems, and digital communications. These