基于稀疏快速傅里叶变换的光纤F-P传感器腔长解调方法

Method of the Cavity Length Demodulation for Optical Fiber F-P Sensors Based on Sparse Fast Fourier Transform

因光纤法布里-珀罗(F-P)传感器的干涉光信号频谱具有稀疏性,求解腔长时,传统的快速傅里叶变换(FFT)算法需要计算整个频率范围内的频谱成分,计算速度较慢。稀疏快速傅里叶变换(SFFT)算法只需计算干涉光信号的主要频谱成分,通过频谱重排、窗函数滤波、频域降采样,以及循环定位与估值,能快速地计算出信号频谱中K个极大的傅里叶系数,从中找出腔长对应的频率,解调出腔长。该算法结构简单,时间复杂度低。通过分析光纤FP传感器腔长解调系统的实际干涉光信号,验证解调结果的准确性,以及相比FFT算法的高效性。因此,SFFT算法适用于对光纤F-P传感器腔长进行在线实时解调,以实时测量物理量。

Because the spectrum of the interference optical signal in optical fiber Fabry-Pérot（F-P）sensor is sparse,the traditional fast Fourier transform（FFT）algorithm needs to calculate the spectrum components in the whole frequency range in the process of solving the cavity length,and the calculation speed is slow.While sparse fast Fourier transform（SFFT）algorithm only needs to calculate the main spectrum components of the interference optical signal.Through rearranging spectrum,filtering with window function,down sampling in frequency domain,and finally looping location and valuation,SFFT can quickly calculate the K maximal Fourier coefficients of the signal spectrum.Thus SFFT can quickly find the frequency corresponding to cavity length and demodulate the cavity length.The algorithm is simple in structure and low in time complexity.It is verified that the accuracy of the demodulation results of SFFT algorithm is better,and the efficiency is faster than that of FFT algorithm by analyzing the actual interference optical signal of optical fiber F-P sensor demodulation system.It is proved that SFFT is very suitable for on-line real-time demodulation of cavity length of optical fiber F-P sensors,so as to measure physical quantities in real time.