The computation of line spectrum pair using modified complex-free Ferrari formula

This paper proposed a fast algorithm for computing the line spectrum pairs (LSP) parameters that are widely used in speech coding systems. The first step of the proposed algorithm is to derive a quartic equation from the 1st derivative of the given 5-degree LSP polynomial. Then the approximate extremes of the 5-degree LSP polynomial can be found by applying the proposed modified complex-free Ferrari's formula to the above quartic equation. By the use of these approximate extremes as the initial approximations, one can easily solve the roots of the 5-degree LSP polynomial via Newton's method and get the accurate LSP parameters. One of main advantages of the proposed algorithm is that the modified complex-free Ferrari's formula can rapidly determine the roots of a quartic equation and resulting in considerable computational saving. In comparison with other methods, the proposed algorithm can determine precise LSP parameters with the lowest computational complexity.