Fast Algorithms for Rapidly Sampled Data

High sampling densities often lead to numerical illconditioning in statistical signal processing algorithms. Reformulation of signal or system dynamics via a delta, or divided-difference, dynamical operator can provide a framework within which the amelioration of such illconditioning can be treated on a formal and unified basis. A number of basic signal-processing problems have been studied in his context over the past decade, and these are reviewed here.

[1]  Faryar Jabbari,et al.  Lattice filters for RLS estimation of a delta operator-based model , 1991 .

[2]  R. Vijayan,et al.  Lattice filters based on the delta operator , 1997 .

[3]  Graham C. Goodwin,et al.  A Levinson-type algorithm for modeling fast-sampled data , 1991 .

[4]  Michel Gevers,et al.  Roundoff noise minimization using delta-operator realizations [digital filters] , 1993, IEEE Trans. Signal Process..

[5]  G. Goodwin,et al.  Connection between continuous and discrete Riccati equations with applications to kalman filtering , 1988 .

[6]  T. Kailath,et al.  On a generalized Szegö- Levinson realization algorithm for optimal linear predictors based on a network synthesis approach , 1978 .

[7]  H. V. Poor.  Differential encoding of high-resolution data , 1995, 1995 International Geoscience and Remote Sensing Symposium, IGARSS '95. Quantitative Remote Sensing for Science and Applications.

[8]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

[9]  Dinh Tuan Pham,et al.  Levinson-Durbin-type algorithms for continuous-time autoregressive models and applications , 1991, Math. Control. Signals Syst..

[10]  M. Morf,et al.  Fast time-invariant implementations of Gaussian signal detectors , 1978, IEEE Trans. Inf. Theory.

[11]  Louis L. Scharf,et al.  Fixed-point error analysis of the lattice and the Schur algorithms for the autocorrelation method of linear prediction , 1989, IEEE Trans. Acoust. Speech Signal Process..

[12]  Hong Fan,et al.  Unequal-length multichannel δb-Levinson and Schur type RLS algorithms , 1995, IEEE Trans. Signal Process..

[13]  Hong Fan,et al.  Delta Levinson and Schur-type RLS algorithms for adaptive signal processing , 1994, IEEE Trans. Signal Process..

[14]  Kamal Premaratne,et al.  Two-dimensional delta-operator formulated discrete-time systems: analysis and synthesis of minimum roundoff noise realizations , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[15]  M. Morf,et al.  Inverses of Toeplitz operators, innovations, and orthogonal polynomials , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[16]  J. L. Roux,et al.  A fixed point computation of partial correlation coefficients , 1977 .