Research on Spectral Restoration and Gas Concentration Inversion Accuracy Based on Quasi-Trapezoidal Window

The Fourier transform is a popular method for analyzing and processing interference data in which spectrum leakage occurs. Generally, window function (also called apodization function) weighting is employed to limit spectrum leakage. A rectangular window with optimal main-lobe performance and the Rife-Vincent (R-V) window were introduced to improve the window function performance, resulting in the establishment of a quasi-trapezoidal window function. Based on the experimental interference data, the quasi-trapezoidal window function was used in the spectral restoration process. The experimental results show that when the apodization degree of the quasi-trapezoidal window was 1.06, the spectral resolution was improved by 17.46% compared with that of the Hanning window; when the apodization degree was 2.71, the spectral signal-to-noise ratio (SNR) was improved by 130.09% compared with that of the Blackman-Harris window function. In the propane (C3H8) and ethylene (C2H4) gas concentration inversion experiment, when the apodization degree was increased from 1.06 to 2.58, the inversion precision was increased by 6.94% for C3H8 gas and 23.93% for C2H4 gas. Through the parameter adjustment, the quasi-trapezoidal window may achieve a high SNR or high-resolution spectral restoration, which can improve the accuracy of gas concentration inversion to some extent.