Super-resolution spectral reconstruction based on minimum variance frequency estimation and linear fitting

Abstract

Fourier transform spectroscopy based on the theory of periodogram or maximum entropy spectral estimation may cause spurious peaks or frequency leakage, as well as distortion of the spectral intensity reconstruction. To solve these problems, spectral reconstruction is treated as an estimation of harmonic frequency and intensity in the interferogram, the super-resolution spectral reconstruction method, based on minimum variance spectral estimation and linear fitting (MVLF), is developed and discussed. MVLF is composed of two steps: frequency estimation with minimum variance frequency estimation and spectral intensity reconstruction with linear fitting. For MVLF, the spectral intensity reconstruction accuracy is only related to frequency estimation accuracy. Simulation results of both discrete and continuous spectral reconstruction show that, compared with traditional super-resolution spectral reconstruction methods, MVLF is able to constrain the frequency estimation error within 0.97% and the spectral intensity reconstruction error within 3%.