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本文的目的在于:1)给出一种非对称Toeplitz线性方程组的快速解法,把这种方法用于ARMA谱AR参数的求解,能比现有的方法减少约1/3的计算量;2)说明了在一定条件下,非对称Toeplitz阵可唯一地三角分解成预测系数阵之积,利用这个结果可方便地计算其逆阵和行列式;3)在此基础上,给出一种把AR参数的求解包含千定阶过程中的ARMA谱快速估算法,并大大降阶了定阶过程的计算复杂性。作者还用数值结果验证了所给算法,并与相应的AR谱估计法作了比较。
The purpose of this paper is to: 1) Give a fast solution to the asymmetric Toeplitz system of linear equations. This method can be used to solve the AR AR spectral parameters, which can reduce the computational complexity by about 1/3 compared with the existing methods. ) Shows that under certain conditions, the asymmetric Toeplitz array can be uniquely triangulated into the product of the predictive coefficient matrix, and the inverse matrix and determinant can be easily calculated using this result. 3) On this basis, The AR parameter solution includes a fast ARMA spectral estimation method in the order of a thousand steps, and significantly reduces the computational complexity of the order process. The author also validates the proposed algorithm with numerical results and compares it with the corresponding AR spectral estimation method.