An efficient VLSI CORDIC array structure implementation of Toeplitz eigensystem solvers

A novel, efficient implementation of the Toeplitz eigensystem solver using a doubly pipelined VLSI CORDIC array processor is presented. First, a backward CORDIC angle recoding scheme is proposed which is able to reduce the number of internal CORDIC iterations by at least 50%. It is shown how to apply this scheme to a family of feedforward algorithms for solving general linear systems, especially the Toeplitz systems. This leads to the implementation of a Toeplitz eigensystem solver with CORDIC-based array processors.<<ETX>>

[1]  J. S. Walther,et al.  A unified algorithm for elementary functions , 1899, AFIPS '71 (Spring).

[2]  B. Anderson,et al.  Asymptotically fast solution of toeplitz and related systems of linear equations , 1980 .

[3]  James Durbin,et al.  The fitting of time series models , 1960 .

[4]  N. Wiener.  The Wiener RMS (Root Mean Square) Error Criterion in Filter Design and Prediction , 1949 .

[5]  Thomas Kailath,et al.  Lattice filter parameterization and modeling of nonstationary processes , 1984, IEEE Trans. Inf. Theory.

[6]  Christopher D. Beatie,et al.  Localization criteria and containment for Rayleigh quotient iteration , 1989 .

[7]  Martin Morf,et al.  Doubling algorithms for Toeplitz and related equations , 1980, ICASSP.

[8]  J. L. Hock,et al.  An exact recursion for the composite nearest‐neighbor degeneracy for a 2×N lattice space , 1984 .

[9]  Sun-Yuan Kung,et al.  A highly concurrent algorithm and pipeleined architecture for solving Toeplitz systems , 1983 .

[10]  David Y. Y. Yun,et al.  Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants , 1980, J. Algorithms.

[11]  K. Jainandunsing,et al.  A new class of parallel algorithms for solving systems of linear equations , 1989 .

[12]  N. Levinson.  The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction , 1946 .

[13]  Philippe Delsarte,et al.  A polynomial approach to the generalized Levinson algorithm based on the Toeplitz distance , 1983, IEEE Trans. Inf. Theory.

[14]  J. Schur,et al.  Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. , 1917 .

[15]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[16]  Yu Hen Hu,et al.  A fast least-square deconvolution algorithm for vocal tract cross section estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[17]  Yu Hen Hu.  Parallel eigenvalue decomposition for Toeplitz and related matrices , 1989, International Conference on Acoustics, Speech, and Signal Processing,.