Modeling local active sound control with remote sensors in spatially random pressure fields.

A general formulation is presented for the optimum controller in an active system for local sound control in a spatially random primary field. The sound field in a control region is selectively attenuated using secondary sources, driven by reference sensors, all of which are potentially remote from this control region. It is shown that the optimal controller is formed of the combination of a least-squares estimation of the primary source signals from the reference signals, and a least-squares controller driven by the primary source signals themselves. The optimum controller is also calculated using the remote microphone technique, in both the frequency and the time domains. The sound field under control is assumed to be stationary and generated by an array of primary sources, whose source strengths are specified using a spectral density matrix. This can easily be used to synthesize a diffuse primary field, if the primary sources are uncorrelated and far from the control region, but can also generate primary fields dominated by contributions from a particular direction, for example, which is shown to significantly affect the shape of the resulting zone of quiet.