A system applicable to acoustic, seismic, electromagnetic, hydrodynamic, and shock waves utilizing a map between signal time series and signal vectors defining the mathematical wave field model characterizing the signal's wave field. This map is developed from wave models relating field values to those on surfaces and corresponding uniqueness theorems. The system should allow for improved resolving power in bearing and elevation for discrimination of sources; detection and direction finding for signals below the average background level; detection based upon resolving power and signal vector characteristics rather than signal to noise ratio; reconstruction of signals of resolved sources for their transmitted information content; and multiple modes of operation. Adaptive incorporation of known undesired signals into the noise background and/or treatment of asymmetric background noise fields is permitted through use of a noise metric-based map yielding signal direction in the presence of diffraction effects.