中文摘要：

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。

英文摘要：

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.