Scharf, Louis L., authorReed, Irving S., authorGoldstein, J. Scott, authorIEEE, publisher2007-01-032007-01-031998Goldstein, J. Scott, Irving S. Reed, and Louis L. Scharf, A Multistage Representation of the Wiener Filter Based on Orthogonal Projections, IEEE Transactions on Information Theory 44, no. 7 (November 1998): 2943-2959.http://hdl.handle.net/10217/744The Wiener filter is analyzed for stationary complex Gaussian signals from an information-theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capability to perform an information-theoretic analysis of previous, basis-dependent, reduced-rank Wiener filters. This analysis demonstrates that the recently introduced cross-spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes. A new reduced-rank Wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal, lower dimensional subspaces. The performance is evaluated using a comparative computer analysis model and it is demonstrated that the low-complexity multistage reduced-rank Wiener filter is capable of outperforming the more complex eigendecomposition-based methods.born digitalarticleseng©1998 IEEE.Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.orthogonal projectionsmutual informationadaptive filteringrank reductionWiener filteringText