Detection of peak wavelength of multi-FBG using higher-order derivative of wavelets multiresolution analysis and maximum likelihood estimation

Abstract

The peak wavelength of fiber Bragg grating (FBG) using the higher-order derivative of Wavelets multiresolution analysis and maximum likelihood estimation is proposed. The FBG reflected spectrum is decomposed at the different level using wavelet multiresolution analysis and the higher-order derivative is applied. The first-order derivative is applied to the calculated desired decomposed level to find the zero-crossing point. The 2nd order derivative is applied and the extrema at the corresponding zero-crossing points are calculated. Further, the proceeding derivative, the 4th order derivative is applied and sharper maxima corresponding zero-crossing point is calculated. The maximum likelihood estimation-based statically method is applied to predict the exact peak wavelengths with good efficiency and low error. The proposed peak detection algorithm is also used in the partially overlapped with weak and non-uniform peaks of cascaded FBGs.