Assuming d sources and m sensors, a generalized formulation is proposed for the direction-of-arrival (DOA) estimation problem. In the generalized formulation a matrix pencil M - lambda N is constructed. For particular values of lambda , the rank of the matrix pencil is decreased by 1. The values of lambda for which this happens provide the information needed to estimate the angles of arrival. The pencil theorem establishes the relationship between these values of lambda and a functional form of the DOAs generated by the operators applied to the measurements. A new angle-of-arrival estimation procedure is formulated in terms of this generalized framework. It makes use of a moving window operator, and is shown to hold for coherent sources.