A solution is obtained to the problem of estimating the number, vector velocity, and waveshape of overlapping planewaves in the presence of interfering planewaves and channel noise, where previous solutions have assumed one or more of these quantities as known. A general optimum solution is not found; instead, a heuristic solution is presented along with a complete working implementation program for large scale computers. For the case where the number of waves and the vector velocities are known, the solution is optimum. The detection of waves and the estimation of their bearing, velocity, and waveshape is accomplished via digital filtering of the frequencywavenumber power spectrum, which is computed via an efficient estimator, of the array sensed data. A new approach to the multiwave estimation problem is to reduce it to a succession of single wave problems using especially developed frequency-wavenumber filters. Special attention is given throughout the study to computationally efficient approaches. The results of the paper are placed in perspective by showing how the historically important approaches to the processing of array data such as delay and sum, weighted delay and sum, array prewhitening, beam forming, inverse filtering, least mean-square estimation, and maximum likelihood estimation are related via the spatio-temporal filtering of the frequency-wavenumber spectrum. The spectral estimation, digital filtering, and the multiwave maximum likelihood estimator developments are demonstrated by the processing of a set of simulated planewaves of various bearings, velocities, and frequencies, as well as by processing electroencephalographic (brain wave) data monitored via an array of scalp electrodes.

The relationship between scalp potentials evoked by visual stimulation and neuronal functioning is examined. A neuronal population model for the electrogenesis of the evoked surface potentials is developed which relies on the hypothesis that the surface potentials are a combination of excitatory post-synaptic potentials (EPSPs) and inhibitory post-synaptic potentials (IPSPs) which occur both at different depths and at different latencies. The model is used to determine the location (depth) of the sources and the approximate size of the neuronal population responsible for the potential. The spatio-temporal potential fields evoked by visual stimulation and monitored by an array of scalp electrodes over the occipital cortex are discussed along with our method for displaying these fields via contour maps. The experimental data are computer simulated via discrete spatially disparate sources. The waveform of each of these sources is determined and the various parameters of the waveform are related to the major characteristics of the spatio-temporal visual evoked potential fields as well as to specific features of the underlying neuronal population. These features include, e.g., the sequence of neuronal excitation, the magnitude of excitatory current, the depth of the neuronal population, and the period of activity of the EPSP and IPSP.

Computer-generated displays of scalp-monitored spatiotemporal potential field patterns evoked by visual stimulation are used to demonstrate that dysfunctions in the visual system can be detected. Such dysfunctions may go unnoticed unless adequate spatial sampling is performed. Various display techniques are presented and discussed. These displays and similar techniques have application in the investigation of numerous and diverse electrophysiological phenomena.