Two-sided unitary transformations of arbitrary 2/spl times/2 matrices are needed in parallel algorithms based on Jacobi-like methods for eigenvalue and singular value decompositions of complex matrices. This paper presents a two-sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required transformations using only the primitives afforded by CORDIC; thus enabling significant speedup in the computation of these transformations on special-purpose processor array architectures implementing Jacobi-like algorithms. We discuss implementation in (nonredundant) CORDIC to motivate and lead up to implementation in the redundant and on-line enhancements to CORDIC. Both variable and constant scale factor redundant (CFR) CORDIC approaches are detailed and it is shown that the transformations may be computed in 10n+/spl delta/ time, where n is the data precision in bits and /spl delta/ is a constant accounting for accumulated on-line delays. A more area-intensive approach using a novel on-line CORDIC encoded angle summation/difference scheme reduces computation time to 6n+/spl delta/. The area/time complexities involved in the various approaches are detailed.>

A two-sided unitary transformation (Q transformation) structured to permit integrated evaluation and application using CORDIC primitives is introduced. The Q transformation is shown to be useful as an atomic operation in parallel arrays for computing the eigenvalue/singular value decomposition of Hermitian/arbitrary matrices, and three specific Q transformations that are needed in such arrays are identified. Issues related to the use of CORDIC for complex arithmetic are addressed, and implementations in both conventional (nonredundant) CORDIC and redundant and online modifications to CORDIC are described. If the time to compute a CORDIC operation in nonredundant CORDIC is T/sub c/, the Q transformations identified here can be evaluated and/or applied in 2T/sub c/ using four CORDIC modules for maximum concurrency. In either case, 0.5 T/sub c/ is required to account for scale factor correction. It is shown that a Q transformation can be evaluated and/or applied in /spl ap/10n, where n is the desired bit-precision.>