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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。
Aiming at the problem that the autocorrelation can not detect the phase in the correlation detection method and the cross correlation requires the reference signal, a self-convolution detection method is proposed based on the correlation and the convolution. Firstly, the relationship between correlation and convolution is extended. Then, the self-convolution of periodic signal, the convolution of two-period signal, the convolution of periodic signal and noise, the self-convolution of noise, the self-convolutional expression It is theoretically proved that the self-convolution detection method can detect the frequency, amplitude and phase of the signal while suppressing the noise. Finally, as a practical example of the self-convolution detection method, a new discrete spectrum correction method is proposed based on the method of energy centroid. The simulation results show that the proposed method can improve the anti-noise performance of discrete spectrum correction, and has certain reference value for the research on the relationship between convolution and convolution.