Fig. 1. Second harmonic signals. (a) Original second harmonic spectrum; (b) Fourier transform frequency distribution of original second harmonic curve; (c) second harmonic spectrum with noise; (d) Fourier transform frequency distribution of noisy second harmonic curve

Fig. 2. Relationship between balance parameter and SNR of the first mode component of the second harmonic signal with different noise intensity. (a) SNR of noise signal is -7.6300 dB; (b) SNR of noise signal is -4.7368 dB; (c) SNR of noise signal is -2.7133 dB; (d) SNR of noise signal is -0.3417 dB; (e) SNR of noise signal is 2.6703 dB; (f) SNR of noise signal is 4.7096 dB; (g) SNR of noise signal is 7.1441 dB; (h) SNR of noise signal is 10.1235 dB

Fig. 3. Intrinsic mode components of noisy signals and their corresponding spectra. (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) frequency distribution of IMF1; (f) frequency distribution of IMF2; (g) frequency distribution of IMF3; (h) frequency distribution of IMF4

Fig. 4. Effect graph of VMD-WTFD

Fig. 5. Denoising effects of different algorithms. (a) EMD-WTFD; (b) EEMD-WTFD; (c) CEEMDAN-WTFD; (d) WTFD

Fig. 6. Relationship between second harmonic amplitude and CO concentration before denoising

Fig. 7. Relationship between second harmonic amplitude and CO concentration after denoising

Table 1. Correlation coefficients between four modal components of noise signal and original signal

Table 2. Comparison of denoising performance of various methods