Denoising of Second Harmonic Signals of the Absorption Spectrum
Using the Frequency Decomposition Combined With the
Savitzky-Golay Filtering
TU Xing-hua, LUAN Xiao-chen, WANG Zhan
College of Electronic and Optical Engineering & College of Flexible Electronics(Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Abstract：To address the issue of noise interference in the detection of second harmonic signals from weak gas absorption spectral lines, this paper proposes a method combining frequency decomposition (FD) and Savitzky-Golay filtering (SG filtering), referred to as FD-SG filtering, to denoise noisy signals. Frequency decomposition is a mathematical method used to decompose complex signals, with the advantage of independently selecting the number of decompositions or solving non-recursively. SG filtering processes groups of data, improving data accuracy while maintaining signal trend and width. The proposed method first applies frequency decomposition to the noisy signal, followed by SG filtering for secondary denoising. Then, it reconstructs the denoised second harmonic signal from the filtered effective components. After frequency decomposition, the distribution of each component is analyzed, confirming that the effective signal mainly resides in the first component but still contains residual noise. By constructing an adjustment factor P to select the optimal SG filter length, the residual noise in the effective component is effectively removed. In experiments with CO2 in the air using an absorption spectral line at 1 578.222 nm, significant noise was found in the second harmonic signal, especially with large spike noise at scan cycle junctions. Fitting curve subtraction and frequency decomposition showed limited noise reduction for large spikes. The combination of SG filtering and the relationship between the second harmonic and spike peak values demonstrated that SG filtering effectively reduces spike noise, achieving ideal denoising with the appropriate filter length. When detecting the second harmonic signal of exhaled CO2, the turbulence caused by exhalation increased and jittered the signal amplitude. FD-SG filtering successfully suppressed the noise, yielding a smoother second harmonic signal. This verifies the algorithm's effectiveness in denoising second harmonic signals for practical weak gas detection, showing significant advantages in noise suppression and large spike noise reduction. This has positive implications for improving signal quality and system accuracy in weak gas detection.
涂兴华，栾小晨，王 战. 吸收光谱线二次谐波的频率分解和SG滤波复合降噪[J]. 光谱学与光谱分析, 2025, 45(05): 1209-1216.
TU Xing-hua, LUAN Xiao-chen, WANG Zhan. Denoising of Second Harmonic Signals of the Absorption Spectrum
Using the Frequency Decomposition Combined With the
Savitzky-Golay Filtering. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2025, 45(05): 1209-1216.
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