中文摘要：

对LPSD算法进行改进,引入有理正交基来替换原来的三角函数基。与三角函数基相比,有理正交基的优势是能自适应地选取基函数的系数。采用能量下降最快的思想和最小均方误差思想逐步求得基函数的系数,然后分解出极小相位信号与全相位信号。与LPSD算法相比,改进后算法比之前在耗时与算法迭代步数上有很大改进,信号拟合效果更好。

英文摘要：

We improve the LPSD algorithm by introducing the rational orthogonal basis to replace thetrigonometric series. Compared with trigonometric series, the advantage of the rational orthogonal basis is that thecoefficients of basis function can adaptively be chosen. In this paper, based on the energy decrease fastestmethod and the least mean square error method, we can choose the coefficients of basis function step by step.Compared with the LPSD algorithm, the improved algorithm has greatly improved the time consuming and thenumber of iteration steps. Moreover, the fitting effect is better than that of LPSD algorithm.