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In single-channel techniques for hands-free acoustic human/machine interfaces, we deal with waveforms which are functions of the continuous time. The aim of multi-channel sound capture is to exploit the structure of propagating waves, i.e., spatial and temporal properties in order to better meet the requirements of speech enhancement. The received signals are thus deterministic functions of position and of time, and, therefore, are called or . They have properties which are governed by the law of physics, in particular the wave equation. Just as temporal filtering can be described by temporal impulse responses, the wave propagation in acoustic environments can be modeled using space-time filters which are described by spatio-temporal impulse responses. Often, the deterministic model of space-time signals cannot be applied to acoustic signals, since audio signals can hardly be described by functions where each time instance is assigned a unique numerical value. The deterministic model of room impulse responses is not appropriate if the spatial extension of the source cannot be neglected since such spatio-temporal impulse responses of acoustic environments can generally not be described analytically. In such situations, it is more convenient to use statistical random .elds which are the ex tension of stochastic processes to multi-dimensional parameter spaces.

In single-channel techniques for hands-free acoustic human/machine interfaces, we deal with waveforms which are functions of the continuous time. The aim of multi-channel sound capture is to exploit the structure of propagating waves, i.e., spatial and temporal properties in order to better meet the requirements of speech enhancement. The received signals are thus deterministic functions of position and of time, and, therefore, are called or . They have properties which are governed by the law of physics, in particular the wave equation. Just as temporal filtering can be described by temporal impulse responses, the wave propagation in acoustic environments can be modeled using space-time filters which are described by spatio-temporal impulse responses. Often, the deterministic model of space-time signals cannot be applied to acoustic signals, since audio signals can hardly be described by functions where each time instance is assigned a unique numerical value. The deterministic model of room impulse responses is not appropriate if the spatial extension of the source cannot be neglected since such spatio-temporal impulse responses of acoustic environments can generally not be described analytically. In such situations, it is more convenient to use statistical random .elds which are the ex tension of stochastic processes to multi-dimensional parameter spaces.