Prony分解的本质及其算法改进的新途径

Prony算法能从均匀采样信号中提取有价值的信息,可分解出一系列按指数衰减的正弦曲线.该算法需要计算最小二乘法拟合和高次代数方程求复根.当信号中嵌入噪声时,Prony求解过程会因方程病态而失败.如输入数据太长,或预估有效模态项数较多,就会造成计算数字溢出.本文方法是:对太长的数据系列采用分段平均值压缩滤波,在求解“法方程”时,能自动确定有效模态的项数,无需SVD奇异值计算,从而大大简化Prony算法、扩大适应范围并确保解算的质量.

The prony method nature and new ways for algorithm improvement

Prony method extracts valuable information from a uniformly sampled signal and builds a series of damped exponentials of sine function. Prony method needs least-squares fitting algorithm and Polynomial algebraic equation to complex roots. When the noise embeds into signal, Prony equation solving process would fail due to these noise. If the input data is too long, or the estimate items number of effective modes is too large, calculations will result in overflow. This paper presents a method by using of sub-average compression filter for long series of data , and then solving the ＂ normal equations＂, can automatically determine the number for effective mode items, without SVD calculate, which greatly simplifies the Prony algorithm to expand the scope to adapt and ensure the quality of solver.