Proceedings ArticleDOI
Hilbert space array methods for finite rank process modeling and ladder form realizations
Carlos H. Muravchik,Martin Morf,D. Lee,J.-m. Delosme +3 more
- Vol. 20, pp 335-339
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TLDR
The application of the array approach to the class of fimte (shift) rank processes is dealt with, which can be applied to a large variety of signal processing problems.Abstract:
We present a Hilbert space array approach for deriving fast estimation and adaptive signal processing algorithms. These are obtained using, as a basic tool, projection operators and orthonormalizations, via the Gram-Schmidt procedure. The resultant algorithms are recursive in time and order, and are realized in ladder forms. The importance of this array method is that it can be applied to a large variety of signal processing problems. This paper deals with the application of our array approach to the class of fimte (shift) rank processes.read more
Citations
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Journal ArticleDOI
Least-squares adaptive lattice and transversal filters: A unified geometric theory
TL;DR: A unified theory is presented to characterize least-Squares adaptive filters, in either lattice or transversal-filter form, for nonstationary processes, based upon a geometric formulation of least-squares estimation and on the concept of displacement rank.
Proceedings ArticleDOI
Generalized CORDIC for digital signal processing
TL;DR: The development of algorithms involving nonstationary processes and the limiting constraints of VLSI motivate the extension of the CORDIC concept in other directions, which can be applied not only to one-parameter groups but to other Lie groups as well, leading to generalized CORDic algorithms.
Proceedings ArticleDOI
Hilbert space array methods for finite rank process estimation and ladder realizations for adaptive signal processing
TL;DR: A Hilbert space array approach for deriving fast estimation and adaptive signal processing algorithms, that are recursive in time and order, that turn out to be the natural realizations of these algorithms.
References
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Journal ArticleDOI
Displacement ranks of matrices and linear equations
TL;DR: In this paper, the concept of displacement ranks is introduced to measure how close a given matrix is to Toeplitz matrices, and it is shown that these non-Toeplitzer matrices should be invertible with a complexity between O(N2 and O(3).
Journal ArticleDOI
Square-root algorithms for least-squares estimation
Martin Morf,Thomas Kailath +1 more
TL;DR: Several new algorithms are presented, and more generally a new approach, to recursive estimation algorithms for linear dynamical systems, based on certain simple geometric interpretations of the overall estimation problem.
Journal ArticleDOI
New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices
TL;DR: By introducting a way of characterizing matrices in terms of their “distance” from being Toeplitz, a natural extension of recursive algorithms for finding the inverses of ToEplitz or displacement-type matrices is obtained.
Analysis chip set based on square- root normalized ladder forms'
TL;DR: The general applicability of the VLSI chip set to other signal processing tasks is demonstrated by showing that the discrete Fourier transform (DFT) is naturally suited to the architecture.