The SVD and reduced rank signal processing

Abstract The basic ideas of reduced-rank signal processing are evident in the original work of Shannon, Bienvenu, Schmidt, and Tufts and Kumaresan. In this paper we extend these ideas to a number of fundamental problems in signal processing by showing that rank reduction may be applied whenever a little distortion may be exchanged for a lot of variance. We derive a number of quantitative rules for reducing the rank of signal models that are used in signal processing algorithms.

[1]  R. Kumaresan,et al.  Singular value decomposition and improved frequency estimation using linear prediction , 1982 .

[2]  S. Applebaum,et al.  Adaptive arrays with main beam constraints , 1976 .

[3]  Louis L. Scharf,et al.  Low rank detectors for Gaussian random vectors , 1987, IEEE Trans. Acoust. Speech Signal Process..

[4]  J. Shanks.  RECURSION FILTERS FOR DIGITAL PROCESSING , 1967 .

[5]  C. T. Mullis,et al.  Quadratic Estimators of the Power Spectrum , 1989 .

[6]  A. Evans,et al.  Optimal least squares time-domain synthesis of recursive digital filters , 1973 .

[7]  Louis L. Scharf,et al.  Reduced rank methods for solving least squares problems , 1989, Twenty-Third Asilomar Conference on Signals, Systems and Computers, 1989..

[8]  H. Akaike.  A new look at the statistical model identification , 1974 .

[9]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[10]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[11]  D. Thomson,et al.  Spectrum estimation and harmonic analysis , 1982, Proceedings of the IEEE.

[12]  Yoram Bresler,et al.  Exact maximum likelihood parameter estimation of superimposed exponential signals in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[13]  Ramdas Kumaresan,et al.  An algorithm for pole-zero modeling and spectral analysis , 1986, IEEE Trans. Acoust. Speech Signal Process..

[14]  Louis L. Scharf,et al.  Rank reduction for modeling stationary signals , 1987, IEEE Trans. Acoust. Speech Signal Process..

[15]  Louis L. Scharf,et al.  Estimation of structured covariance matrices and multiple window spectrum analysis , 1990, IEEE Trans. Acoust. Speech Signal Process..

[16]  L. J. Griffiths,et al.  An alternative approach to linearly constrained adaptive beamforming , 1982 .

[17]  G. Bienvenu,et al.  Principe de la goniometrie passive adaptative , 1979 .

[18]  E. Parzen.  Some recent advances in time series modeling , 1974 .

[19]  H. Zeiger,et al.  Approximate linear realizations of given dimension via Ho's algorithm , 1974 .

[20]  R. Kumaresan,et al.  Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise , 1982 .

[21]  Edward J. Wegman,et al.  Statistical Signal Processing , 1985 .