Norbert Wiener the amount of noise present in a signal by comparison with an estimate of the desired noiseless signal. Wiener developed the filter at the Radiation Laboratory at MIT to predict the position of German bombers from radar reflections. It is necessary to predict the future, because by the time the shell reaches the vicinity of the target, the target has moved, and maybe has changed direction slightly. They even modeled the muscle response of the pilot, which led eventually to cybernetics. The unmanned V1's were particularly easy to model, and on a good day, American guns fitted with Wiener filters
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