Fast Approximation of Dominant Harmonics
Fast Approximation of Dominant Harmonics
复制标题
主谐波的快速逼近
DOI：
10.1137/0905024
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
G. Cybenko
中科院分区：
文献类型：
--
作者：
G. Cybenko
本文提出了一种快速估计数据序列中主谐波的方法。在随机意义上，所提出的方法发现的自回归计划与纯点谱，最好地描述了数据，而从确定性的角度来看，该方法是一个特殊的情况下，Lanczos算法寻找对称矩阵的特征值。特征值近似开始起作用，因为每个循环矩阵都被离散傅立叶变换矩阵对角化，因此使用Lanczos算法，给定数据作为简单循环矩阵上的初始向量，首先近似的特征值是对应于初始向量中占主导地位的特征向量的特征值。它表明，这种方法是有关的“格方法”的线性预测和Prony的方法的指数逼近。
This paper presents a fast method for estimating dominant harmonics in a sequence of data. In a stochastic sense, the proposed method finds the autoregressive scheme with a pure point spectrum that best describes the data, while from a deterministic point of view, the method is a special case of the Lanczos algorithm for finding eigenvalues of a symmetric matrix. Eigenvalue approximations come into play because every circulant matrix is diagonalized by the discrete Fourier transform matrix, and so using the Lanczos algorithm with the given data as the initial vector on a simple circulant matrix, the eigenvalues that are first approximated are the eigenvalues corresponding to eigenvectors which are dominant in the initial vector. It is shown that this method is related to “lattice methods” for linear prediction and to Prony’s method for exponential approximation.