结合牛顿-拉夫森函数计算语音线谱对参数的高效算法

提出了计算语音信号线谱对（LSP）参数的高效算法NRSPF。首先利用牛顿法-拉夫森函数及斯蒂芬森加速求高阶非线性方程的一个实根，再使用多项式综合除法降阶，最后采用费拉里算法求其余的根，即得LSP参数。通过TI-DSP平台的实例研究表明，NRSPF算法与APF算法相比，迭代次数减少、收敛速度加快，计算量小，并且在精度提高10倍、100倍和1000倍情况下，APF算法可能出现被零除错误和死循环，而NRSPF算法不仅避免了该错误，而且迭代次数增加很少，收敛速度仍然很快，得到更精确的结果。本文提出的算法高效、可靠、实时性强，可应用于超低码率语音实时通信系统、语音编解码器等。 

An Efficient Algorithm for Calculating LSP Parameters of Speech Combined with Newton-Raphson Function

This paper proposed an efficient algorithm NRSPF for calculating line spectrum pairs(LSP) parameters of speech signal. LSP parameters can be estimated by obtaining a root of high order nonlinear equation by Newton-Raphson function and Steffensen acceleration at first, then decreasing degrees with polynomial synthesis division, finally calculating other roots using Ferrari’s solution. Through analysis of practical example on TI-DSP, we found that NRSPF algorithm reduced the number of iterations, accelerated convergence rate and had small amount of calculation when compared with APF algorithm. In the case of precision increasing 10 times, 100 times and 1000times, APF algorithm maybe occurred division by-zero error and infinite loop while NRSPF algorithm not only avoided the error, but increased very few of iterations, got more accurate results, the convergence speed was still fast. The proposed algorithm has high performance, reliablity, strong real-time, which can be applied to low-bit rate real-time speech transmission system, speech encoding and decoding system, etc.