NDLI: Recursive least-squares lattices and trigonometry in the spherical triangle

Content Provider	IEEE Xplore Digital Library
Author	Desbouvries, F.
Copyright Year	1993
Description	Author affiliation: Inst. Nat. des Telecommun., Evry, France (Desbouvries, F.)
Abstract	The three fundamental planar biorthogonalization steps which underlie the geometric derivation of the fast recursive least squares (FRLS) adaptive lattices are gathered into a unit-length 3-D tetrahedron. The inverse of Yule's PARCOR Identity (YPII) then admits a nice geometric interpretation in terms of projections into this tetrahedron. Since tetrahedrons are closely related to spherical triangles, YPII is recognized as the fundamental 'cosine law' of spherical trigonometry. In that framework, the angle-normalized RLS lattice recursions happen to be one particular solution to one of the six spherical triangle problems. The practical interest of this geometric interpretation is that one can take advantage of spherical trigonometry to derive unnoticed recursions among RLS quantities. This leads, for instance, to an original 'dual' version of YPII.<>
Starting Page	404
Ending Page	407
File Size	374918
Page Count	4
File Format	PDF
ISBN	0780374029
ISSN	15206149
DOI	10.1109/ICASSP.1993.319520
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1993-04-27
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lattices Resonance light scattering Vectors Transversal filters Delay effects Error correction Equations Hilbert space Random variables Adaptive filters
Content Type	Text
Resource Type	Article

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