A rootfinding algorithm for line spectral frequencies

Published techniques for computing line spectral frequencies (LSFs) generally avoid rootfinding methods because of concerns about convergence and complexity. However, this paper shows that stable predictor polynomials have properties that make rootfinding an attractive approach. It is well known that the problem of finding the LSFs for an N´th order predictor polynomial can be reduced to the problem of finding the roots of a pair of polynomials of order N/2 with real roots. The author extends this result by showing that these polynomials have the following properties: 1. It is possible to select starting points for a Newton´s rootfinding method such that the iteration will converge monotonically to the largest root. 2. The Newton iteration can be modified to speed up the process while still maintaining good convergence properties. In this paper, the author presents the rootfinding procedures with proofs of their good convergence properties. Finally, he presents experimental results showing that this procedure performs well on speech signals, and that it can be implemented on fixed-point DSPs