New Split Levinson, Schur, and Lattice Algorithms for Digital Signal Processing

摘要

In this work, we analyze the mathematical structure associated with the split algorithms for computing the reflection coefficients for a given real, symmetric, positive-definite Toeplitz matrix. A new form of three-term recurrence relation is derived and computationally efficient alternatives to the Levinson-Durbin, Schur, and lattice algorithms are obtained. The computational complexity of the new algorithms is the same as those of the split algorithms described in the recent literature. These algorithms also provide further insight into the mathematical properties of the structurally rich Toeplitz matrices. Reprints. (rh)