强噪声背景下基于小波变换的正弦信号参数估计算法研究

发布时间：2018-11-03 12:29

【摘要】：在通信领域与信号处理中,微弱正弦信号的参数估计是一个基础性的并且被大量研究的问题。当前,微弱正弦信号的参数估计已经被广泛的应用于信号恢复、语音信号处理、雷达目标定位等诸多领域。因此,对于微弱正弦信号的参数估计问题的研究具有重要的理论意义与实际应用价值。本文对DFT算法、最小二乘算法进行了分析,对于微弱正弦信号,这些算法的估计值与真实值相差较大。针对此问题,本文对DFT算法和最小二乘法进行改进,分别得到了基于DFT和DWT的频率估计算法,基于DWT的相位估计算法及改进的幅值算法。本文的主要工作如下:1.给出了DFT频率估计的改进算法。该算法提高了频率估计的精度,公式推导比较简单,同时改进算法的计算量低于DFT算法的计算量,易于工程实现;2.给出了基于离散小波变换的频率估计算法以及频率校正的迭代算法。使用小波变换对信号进行处理,从而获得两段新的序列,对获得的两段不同长度的序列分别实施离散傅里叶变换,通过推导得到频率的粗估计值,在此基础上,给出了频率校正的迭代算法,并对性能进行了分析;3.给出了基于DWT的相位估计算法。利用小波变换对信号处理,得到长度不同的序列,并对得到的序列实施Z变换,结合序列的构造方式通过推导得到相位的估计值。将该算法与以往算法进行仿真实验对比,可以看出在低信噪比下,该算法有较好的估计精度;4.给出了正弦信号幅值估计算法。并将此算法与基于自相关函数的幅值估计进行仿真实验对比了,可以看出该算法具有较高的估计精度。
[Abstract]:In the field of communication and signal processing, the parameter estimation of weak sinusoidal signal is a basic and widely studied problem. At present, the parameter estimation of weak sinusoidal signal has been widely used in many fields, such as signal recovery, speech signal processing, radar target location and so on. Therefore, the research on parameter estimation of weak sinusoidal signal has important theoretical significance and practical application value. In this paper, the DFT algorithm and the least square algorithm are analyzed. For the weak sinusoidal signal, the estimated value of these algorithms is quite different from the real value. In order to solve this problem, the DFT algorithm and the least square method are improved in this paper. The frequency estimation algorithms based on DFT and DWT, the phase estimation algorithm based on DWT and the improved amplitude algorithm are obtained, respectively. The main work of this paper is as follows: 1. An improved algorithm for DFT frequency estimation is presented. The algorithm improves the accuracy of frequency estimation, and the formula derivation is relatively simple, and the computational complexity of the improved algorithm is lower than that of DFT algorithm, which is easy to be realized in engineering. 2. A frequency estimation algorithm based on discrete wavelet transform and an iterative algorithm for frequency correction are presented. The wavelet transform is used to process the signal, and two new sequences are obtained. The discrete Fourier transform is applied to the two sequences of different lengths, and the coarse estimation of the frequency is derived. The iterative algorithm of frequency correction is given, and the performance is analyzed. 3. A phase estimation algorithm based on DWT is presented. The wavelet transform is used to process the signal and the sequence of different length is obtained. The Z transform is applied to the sequence and the phase estimation is obtained by deducing the method of constructing the sequence. By comparing the algorithm with the previous algorithms, we can see that the algorithm has better estimation accuracy under low SNR. 4. An algorithm for estimating the amplitude of sinusoidal signals is presented. By comparing this algorithm with the amplitude estimation based on autocorrelation function, it can be seen that the algorithm has high estimation accuracy.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23

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