Fourier and wavelet transform analysis of wavelength modulation spectroscopy signal

In the present paper, the performances of an approach based on continuous wavelet transform to demodulate wavelength modulation spectroscopy harmonic signal (CWT-WMS) have been compared to the conventional approach using digital lock-in amplifier (DLI-WMS) based on classic Fourier transform analysis. For both methods, consistent results were obtained and good agreement between the experimental and simulated results was observed. The CWT method does not require the use of a reference signal and the phase-insensitive harmonic signals are directly obtained. The CWT method also demonstrates higher signal-to-noise ratio (SNR) and better temporal coherence than the DLI-WMS approach. The results obtained in the present study for CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{CO}_{{2}}$$\end{document} in a gas cell and in a previous study for H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{H}_{{2}}$$\end{document}O in a laminar flame tend to indicate that the parameters of the CWT-WMS method could be used for a large variety of experimental conditions and target species without requiring important adjustment. On the other hand, the DLI-WMS method presents a benefit in term of computational time which is 47.9%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$47.9\%$$\end{document} shorter than for the CWT-WMS.