Two-level method using a decimation-in-degree algorithm for the computation of the LSP frequencies

A two-level method is proposed in this study for rapidly and accurately computing the line spectrum pair (LSP) frequencies. An efficient decimation-in-degree (DID) algorithm is also proposed in the first level which can transform any symmetric or antisymmetric polynomial with real coefficients into the other polynomials with lower degrees and without any transcendental functions. The DID algorithm not only can avoid prior storage or large calculation of transcendental functions but can also be easily applied towards those fast root-finding methods. In the second level, the Newton-Raphson method is applied. The process of the Newton-Raphson method can be accelerated by adopting a deflation scheme along with the interlacing property of LSP frequencies for selecting the better initial values. A few conventional numerical methods are also implemented to make a comparison with the two-level method. Experimental results indicate that the two-level method is the fastest one.