Spherical trigonometry, Yule's Parcor identity, and FRLS fully normalized lattice

François Desbouvries

doi:10.1109/78.485939

Spherical trigonometry, Yule's Parcor identity, and FRLS fully normalized lattice

François Desbouvries

CNRS SAMOVAR UMR 5157

Research output: Contribution to journal › Article › peer-review

Abstract

Yule's PARCOR identity is recognized as the cosine law of spherical trigonometry. The six PARCORs propagated by the fullly normalized FRLS lattice filter are the cosines of the six elements of a spherical triangle, and this lattice algorithm is one solution to a spherical triangle problem that arises naturally in navigation and astronomy. Exploiting this new geometric interpretation yields unnoticed (and potentially useful) recursions among FRLS quantities.

Original language	English
Pages (from-to)	427-430
Number of pages	4
Journal	IEEE Transactions on Signal Processing
Volume	44
Issue number	2
DOIs	https://doi.org/10.1109/78.485939
Publication status	Published - 1 Dec 1996
Externally published	Yes

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abstract = "Yule's PARCOR identity is recognized as the cosine law of spherical trigonometry. The six PARCORs propagated by the fullly normalized FRLS lattice filter are the cosines of the six elements of a spherical triangle, and this lattice algorithm is one solution to a spherical triangle problem that arises naturally in navigation and astronomy. Exploiting this new geometric interpretation yields unnoticed (and potentially useful) recursions among FRLS quantities.",

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AB - Yule's PARCOR identity is recognized as the cosine law of spherical trigonometry. The six PARCORs propagated by the fullly normalized FRLS lattice filter are the cosines of the six elements of a spherical triangle, and this lattice algorithm is one solution to a spherical triangle problem that arises naturally in navigation and astronomy. Exploiting this new geometric interpretation yields unnoticed (and potentially useful) recursions among FRLS quantities.

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Spherical trigonometry, Yule's Parcor identity, and FRLS fully normalized lattice

Abstract

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