A qualitative and quantitative theory is developed which simultaneously unifies and extends MUSIC, MIN-NORM, ESPRIT, and PISARENKO type techniques. These techniques can be used for both spatial and temporal spectral decomposition of signals. In particular, the usual assumptions on the problem formulation are reduced. Our approach is a realization theoretic approach and substantially extends the previous results on multidimensional arrays of sensors. A theory is provided for analysis and design of (not necessarily linear and equally spaced) array structures to estimate the temporal frequency and the directions for coherent sources, such as in the case of multipath. Techniques are also developed to null signals in certain directions with certain frequencies, such as for multipath cancellation.