Azimi-Sadjadi, Mahmood R., authorScharf, Louis L., authorPezeshki, Ali, authorHua, Yingbo, 1960-, authorIEEE, publisher2007-01-032007-01-032005Pezeshki, Ali, et al., Two-Channel Constrained Least Squares Problems: Solutions Using Power Methods and Connections with Canonical Coordinates, IEEE Transactions on Signal Processing 53, no. 1 (January 2005): 121-135.http://hdl.handle.net/10217/1013The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering and transform methods for resolving channel measurements into canonical or half-canonical coordinates. Based on this connection, a unified framework for reduced-rank Wiener filtering is presented. Then, various representations of reduced-rank Wiener filters in canonical and half-canonical coordinates are introduced. An alternating power method is proposed to recursively compute the canonical coordinate and half-canonical coordinate mappings. A deflation process is introduced to extract the mappings associated with the dominant coordinates. The correctness of the alternating power method is demonstrated on a synthesized data set, and conclusions are drawn.born digitalarticleseng©2005 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.generalized eigenvalue problemconstrained least squarescanonical coordinatesalternating power methodhalf-canonical coordinatesreduced-rank Wiener filteringrank reductionSVDtwo-channel least squaresText