M周期分数傅里叶变换的光栅信号去噪方法

Grating signal denoising method with M-cycle Fractional Fourier Transform

用矩阵方法离散地实现了任意M周期的分数傅里叶变换(FRFT),它可实现变换级次及周期的自由选择。根据相应的噪声频谱,选取适当的级次及周期,可使FRFT构造一个极窄的带阻滤波器,将其中心频率对准相应噪声的窄谱,便可滤除与理想信号频谱重叠部分的噪声分量,同时保持信号分量。在实验中,用矩阵方法实现的FRFT对所测光栅信号进行了去噪处理,并与传统的傅里叶与小波分析去噪方法进行了对比,结果表明,只要选取适当的级次和周期(α=0.545,Μ=5)就可获得理想的去噪效果。

The matrix method is introduced to realize the Fractional Fourier Transforms （FRFT） of arbitrary M-cycle discretely, whose transform power （a） and cycle （34） are selected freely. With the method, the value of α and M can be decided with corresponding spectrum of noise. A sharply narrow Band-stop Filter can be constructed by FRFT with reasonable values of a and M. By its central frequency being equal to that of the narrow spectrum of noise, the noise portion overlapped with the ideal signal spectrum is eliminated, while the required signal is well kept. In the experiment, we used FRFT realized with the matrix method to denoise the grating signal and compare it with traditional Fourier and Wavelet denoising methods. As a result, we find that the perfect effect will be acquired as long as reasonable values of power and cycle （α=0.545, M=5） are chosen.