New split Levinson, Schur, and lattice algorithms for digital signal processing

The mathematical structure associated with the split algorithms for computing the reflection coefficients for a given real symmetric positive-definite Toeplitz matrix is analyzed. A novel 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 proposed algorithms is the same as those of the split algorithms described in recent literature. These algorithms provide further insight into the mathematical properties of the structurally rich Toeplitz matrices