Harmonic Extraction Method With Continuous Wavelet Transform Based on the Prior Knowledge of Wavelength Modulation Spectroscopy and Shift Strategy

This article proposes a novel harmonic extraction method with continuous wavelet transform (CWT) based on prior knowledge of wavelength modulation spectroscopy (WMS) and shift strategy (PK-S-CWT). In the proposed method, the simulated transmittance and derived second harmonic (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2{f}$ </tex-math></inline-formula>) are utilized as prior knowledge to construct the mother wavelet function (MWF) of CWT. Due to its amplitude and phase similarity with target harmonics in the frequency domain, useful information can be significantly amplified while maintaining equivalent in-band noise levels, ultimately achieving an improved signal-to-noise ratio (SNR). Meanwhile, with prior knowledge, the optimal frequency scale parameters in CWT can be determined directly, avoiding the cumbersome filter optimization in conventional lock-in filter methods and CWT methods. Furthermore, in the construction of daughter wavelet function (DWF), the shift strategy is employed to decouple the central frequency and half-width of DWF and, thus, effectively solve the harmonic aliasing issues in conventional CWT methods. Simulations and experiments of N2O measurements were conducted to validate the proposed method. The results show that PK-S-CWT outperforms other methods (conventional lock-in filter and other CWT methods) in various aspects, including SNR, linearity of the harmonic amplitude with gas concentration, and accuracy of gas parameters retrieval.