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In the analysis of time/frequency domain signals, lattice filters have proved popular, providing significant advantages over conventional tapped delay line digital filters. Improvements in adaptation times and model order identification have been observed, and the modular structure of these filters allows a straightforward VLSI hardware implementation. In the paper, a lattice-structured spatial filter for use in adaptive arrays is described. This filter is shown to take on a triangular structure in the spatial domain which provides a step-by-step solution to the prediction problem. Several uses of the lattice filter in array processing are then discussed, particularly the extraction of high-resolution spatial spectral estimates from the parameters of the filter. These spatial spectral estimators include the maximum-entropy, maximum-likelihood and eigenvector (Pisarenko) based methods and are used to obtain high-resolution maps of the directional power incident upon an array of spatially distributed sensors. It is also shown how multiple look direction constraints may be applied to the lattice filter, providing the capability for enhancing desired signals in the presence of directional interference.