The mutual information function and its application to signal processing / von Hans-Peter Bernhard

• VerfasserIn: Bernhard, Hans-Peter
• Place / Publishing House: 1997
• Year of Publication: 1997
• Language: English
• Physical Description: 104 Bl.; Ill., graph. Darst.

eng: In this thesis, we introduce a new signal analysis method: the mutual information function. It is designed to deal with output signals of nonlinear systems, unlike the correlation function which reflects only linear system properties. We use the mutual information function to analyze speech signals with the aim of developing a new modeling concept for voiced speech based on nonlinear systems theory. With this method, we determine the dimensionality and dynamic behavior of a low- (4- to 5-) dimensional, deterministic nonlinear oscillator as a new model concept that improves on the prevalent linear source-filter model. A theorem is derived that provides a tight upper bound on the prediction gain of linear and nonlinear predictors for stationary stochastic processes. This very general approach is applied to different system types and their output processes. We illustrate how the mutual information function can be used to compute this bound for several examples. In an energy management systems application, we show the capability of the mutual information function to estimate the maximum prediction gain for load curve forecasting. By input variable selection we could show that just 5 input variables are sufficient to achieve a prediction gain which lies above the gain of linear forecasting systems which rely on more than 100 input variables. As the signal processing core of our approach, we have developed a fast algorithm for the estimation of the mutual information function for a given single realization of a stationary process.