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The paper describes a framework in the form of an optimization of a performance index subject to the constraints of a dynamic network, represented in the state space. The performance index is a measure of statistical dependence among the outputs of the network, namely, the relative entropy also known as the Kullback-Leibler divergence. The network is represented as (either discrete or continuous time) state space dynamics. Update laws are derived in the general cases. Moreover, in the discrete-time case, they are shown to specialize to the FIR and IIR network representations.

Abstract-The paper presents a formulation and an implementation of a system for voice output extraction (VOX) in real-time and near-real-time realistic real-world applications. A key component includes voice-signal separation and recovery from a mixture in practical environments. The signal separation and extraction component includes several algorithmic modules with a variety of sophistication levels, which include dynamic processing neural networks in tandem with (dynamic) adaptive methods. These adaptive methods make use of optimization theory subject to the dynamic network constraints to enable practical algorithms. The underlying technology platforms used in the compiled VOX software can significantly facilitate the embedding of speech recognition into many environments. Two demonstrations are described: one is PC-based and is near-realtime, the second is digital signal processing based and is real time. Sample results are described to quantify the performance of the overall systems.Index Terms-Adaptive networks, audio signal processing, DSP, gradient descent, independent component analysis, neural networks, nonlinear networks and systems, optimization, speech processing, state-space models, statistical independence criteria.

This wot-k presents iI pt-iIcticiIl l'ed time esecution of a family of dynamic blind signal separation slgorithms using commercial digital signal processors (DSP). The implementation adopts discrete-time formulations with a .ckw towards on line commercial use. iil)l)lications esist in voice based computer interfaces and telephony.