On the geometric sequences of reflection coefficients

On the geometric sequences of reflection coefficients

It is shown that a decaying geometric sequence of reflection coefficients corresponds to a predictor polynomial that has all of its roots on a circle centered at the origin of the complex z plane. It is shown that the radius of this circle is equal to the magnitude of the ratio of any two consecutiv...

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Veröffentlicht in:IEEE transactions on acoustics, speech, and signal processing speech, and signal processing, 1990-10, Vol.38 (10), p.1810-1812
Hauptverfasser: Mazel, D.S., Geronimo, J.S., Hayes, M.H.
Format: Artikel
Sprache:eng
Schlagworte:
Acoustic signal processing
Eigenvalues and eigenfunctions
Mathematics
Polynomials
Reflection
Speech
Symmetric matrices
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Zusammenfassung:It is shown that a decaying geometric sequence of reflection coefficients corresponds to a predictor polynomial that has all of its roots on a circle centered at the origin of the complex z plane. It is shown that the radius of this circle is equal to the magnitude of the ratio of any two consecutive terms in the geometric sequence.< >
ISSN:0096-3518
DOI:10.1109/29.60115