Bebe and Louis Barron and the Machine", by mathematician Norbert Wiener from MIT played an important role in the development of the Barrons' composition. The science of cybernetics proposes that certain natural laws of behavior apply to both animals and more complex electronic machines. By following the equations presented in the book, Louis was able to build electronic circuits which he manipulated to generate sounds. Most of the tonalities were generated with a circuit called a ring modulator. The sounds and patterns that came out of the circuits were unique and unpredictable because they were actually overloading the circuits until they burned out to
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