Enhanced Rational Signal Modeling

Abstract In various signal processing applications involving theoretical or empirical considerations, it is desired to appropriately modify a given data set so that the modified data set possesses prescribed properties. These properties are usually chosen so as to identify information signals believed to be contained within the given data set. The modification of the given data set then serves as a cleansing process whereby corrupting noise, measurement distortion or theoretical mismatch present in the given data set is removed. In this paper, a recently developed signal enhancement algorithm is described which achieves this objective. Particular attention is directed towards properties that are describable using a singular value decomposition (SVD) of a data generated matrix. Examples are given demonstrating a significant improvement in the performance of subspace-based frequency estimation techniques. Next, the behavior of these high resolution algorithms with respect to the relative phase of closely spaced sinusoids is examined. This behavior is related to the singular values of the data matrix. The predicted behavior is confirmed in the examples.