乘性和加性噪声中谐波恢复的循环统计量方法

本文从循环平衡的观点出发来研究乘性和加性噪声中的谐波恢复问题.首先，在一定条件下建立了一般复过程的有限长付里叶变换的大样本性质．然后，得到了任意阶循环矩的样本估计关于循环频率的一致收敛速度．对于乘性和加性噪声中的谐波信号，建立了一、二、三阶循环矩样本估计的统计性质．在此基础上，分别提出了基于不同阶循环矩的谐波分最个数和频率的估计方法，并得到了估计的强相容性质和强收敛速度，最后给出了模拟实验结果．

Cyclic Statistics Based Approach to Harmonic Retrieval in Multiplicative and Additive Noise

The harmonics retrieval in multiplicative and additive noise is studied from the view point of cyclostatiolnary processes. At first, the large sample property of the finite Fourier transform for generally complex-valued processes is established under certain mixing conditions. Then, the inliformly convergent rale of any other sample cyclic-moments of cyclostationary processes is obtained. For harmonics in multiplicative and additive noise, the statistical properties of the kth-culer sample cyclic-moments are obtained for k = 1, 2, 3. The estimation for harmonics parameters based on different culer cyclic-moments are presented. The strong convergeneand convergence rate of the estimators are obtained. Finally, the simulation results are given.