自卷积检测方法及其在离散频谱校正中的应用  

Self-convolution Detection Method and Its Application in Discrete Spectrum Correction

作　　者：曾金芳[1] 滕召胜[1] 唐求[1] 

机构地区：[1]湖南大学电气与信息工程学院,湖南省长沙市410082

出　　处：《中国电机工程学报》2014年第28期4976-4982,共7页Proceedings of the CSEE

基　　金：国家自然科学基金项目(51277058);湖南省教育厅项目(13C931)~~

摘　　要：针对相关检测方法中自相关不能检测相位、互相关需要参考信号的问题,从相关和卷积的关系出发,提出一种自卷积检测方法。首先,扩展相关和卷积的关系;然后,分别推导周期信号的自卷积、两周期信号的卷积、周期信号与噪声的卷积、噪声的自卷积、加噪信号的自卷积表达式,从理论上证明自卷积检测方法能检测信号的频率、幅值和相位,同时可以抑制噪声。最后,作为自卷积检测方法的应用实例,结合能量重心法提出一种新的离散频谱校正方法。仿真结果表明,所提方法能提高离散频谱校正的抗噪性能,对研究相关与卷积的关系以及卷积应用有一定的参考价值。Since the correlation detection method has some problems that the autocorrelation method fails to detect the signal＇s phase and the cross-correlation method needs a reference signal, a self-convolution detection method was presented based on the relationship between the correlation and convolution. First, the relationship between the correlation and convolution was extended. Then, expressions of the self-convolution of a periodic signal, the convolution between two periodic signals, the convolution between a periodic signal and noise, the self-convolution of noise, and the self-convolution of a noisy signal were deduced, which illustrated that the self-convolution detection method could detect the frequency, amplitude, and phase of a signal with suppressing noise in theory. Lastly, as an application example of the proposed self-convolution detection method, a novel discrete spectrum correction method was presented combining with the energy centroid method. The simulation results showed that the proposed method could improve the anti-noise performance of spectrum correction. The proposed method has some reference value for studying the relationship between the correlation and convolution and the application of convolution.

关 键 词：信号检测 频谱校正 自卷积 自相关 能量重心法 

分 类 号：TN911.23[电子电信—通信与信息系统]