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Reconstruction of a positive definite Toeplitz matrix from its sequence of minimum eigenvalues
Clements, M.A.; Isabelle, S.H.;
Acoustics, Speech and Signal Processing, IEEE Transactions on
Volume 36,
Issue 11,
Nov. 1988
Page(s):1784
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1786
Abstract:
It is shown that a positive definite symmetric Toeplitz matrix of rank p+1 can be represented uniquely by the minimum eigenvalues of itself and its p submatrices, along with a sign bit for each eigenvalue. The application of such a procedure allows specification of linear prediction coding (LPC) spectra by an alternate set of parameters. It also enables extension of an autocorrelation sequence using a nonstandard criterion. A number of parallels are made between these parameters and the LPC mean-square error values for successively higher-order systems. An application involving maximum entropy spectral estimation under a nonstandard set of constraints is presented
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