Efficient algorithm to compute LSP parameters from 10th-order LPC coefficients

Line Spectrum Pair (LSP) representation of Linear Predictive Coding (LPC) parameters is widely used in speech coding applications. An efficient method for LPC to LSP conversion is Kabal’s method. In this method the LSPs are the roots of two polynomials P'_p(x) and Q'_p(x), and are found by a zero crossing search followed by successive bisections and interpolation. The precision of the obtained LSPs is higher than required by most applications, but the number of bisections cannot be decreased without compromising the zero crossing search. In this paper, it is shown that, in the case of 10th-order LPC, five intervals containing each only one zero crossing of P'₁₀(x) and one zero crossing of Q'₁₀(x) can be calculated, avoiding the zero crossing search. This allows a trade-off between LSP precision and computational complexity resulting in considerable computational saving.