Title :
On the geometric sequences of reflection coefficients
Author :
Mazel, David S. ; Geronimo, Jeffery S. ; Hayes, Monson H., III
Author_Institution :
Georgia Inst. of Technol., Atlanta, GA, USA
fDate :
10/1/1990 12:00:00 AM
Abstract :
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
Keywords :
correlation theory; poles and zeros; polynomials; complex z plane; decaying geometric sequence; predictor polynomial; reflection coefficients; Acoustic signal processing; Eigenvalues and eigenfunctions; Mathematics; Polynomials; Reflection; Speech; Symmetric matrices;
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
