For some signal processing systems, nonlinearity is an essential component: classical examples for nonlinear memoryless systems are quantizers and pattern classifiers. For nonlinear dynamical systems (such as oscillators, filters etc.), the conventional approach to their analysis and design has been linearization as seen e.g. in the field of adaptive filtering. Our focus is to integrate emergent techniques from chaos theory, parallel distributed processing, and nonlinear statistics to arrive at a complete methodological toolbox for nonlinear digital signal processing.
We develop analysis methods that reveal nonlinear signal properties such as dimensionality, information production rate, or local/global stability.
Neural Networks constitute a versatile tool for both static nonlinearities - e.g. pattern classification for automatic speech or image recognition - and dynamic nonlinearities -e.g. time-delay neural networks for channel equalization in digital communication systems. Their architecture is based on parallel distributed processing concepts and, therefore, most attractive for high-speed and/or high-complexity applications. We have experience with neural network applications to noise reduction and signal enhancement, isolated word recognition, and maximum-likelihood sequence detection. Algorithmic developments include Kalman-filtering based learning algorithms and an efficient subspace filtering approach.
Nonlinear Statistics includes concepts such as nonlinear statistical signal modeling, higher-order statistics analysis, and order-statistic filtering. We develop and analyze new methods to implement them efficiently on digital signal processors.