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许多信号处理问题归结为求解一线性方程组。对此线性方程组的系数矩阵进行可能的特性映象,比如低秩化和Toeplitz结构化的处理,可以明显地降低噪声的影响,提高信号参量估计的准确度。本文讨论了数据矩阵的特性映象,并给出了叠代映象系列收敛的简单而形象的证明。在线谱估计的应用中,从正弦波自相关函数的模型出发,推导了该情况下数据矩阵的特性映象算法。通过一实例的计算和比较,可以看出此方法显著地改善了谱估计的性能。
Many signal processing problems boil down to solving a system of linear equations. The possible characteristic maps of the coefficient matrix of the linear equations, such as low-rank and Toeplitz structures, can obviously reduce the influence of noise and improve the accuracy of signal parameter estimation. In this paper, we discuss the characteristic mappings of data matrices and give a simple but vivid proof of the series convergence of iterative mappings. In the application of on-line spectral estimation, from the model of sine wave autocorrelation function, the characteristic mapping algorithm of data matrix in this case is deduced. Through the calculation and comparison of an example, it can be seen that this method significantly improves the performance of spectral estimation.