Denoising Algorithm of Spectral Signal Based on FFT SVD
ZHU Hong-qiu1, CHENG Fei1, HU Hao-nan1, ZHOU Can1, 2*, LI Yong-gang1
1. School of Automation, Central South University, Changsha 410083, China
2. The State Key Laboratory of High Performance Complex Manufacturing, Changsha 410083, China
Abstract：In the process of collecting spectrum signals, the spectrum data is often interfered with by the optical system and electronic circuit of the instrument, which results in noise and characteristic peaks of the light source, and seriously interferes with the spectrum characteristic of the real spectrum signal. Therefore, it is necessary to use a reasonable preprocessing method to retain the useful signal in the spectrum signal, filter the noise signal as much as possible and filter the light source characteristic peak to improve the robustness and accuracy of the quantitative analysis of spectral information. Spectrum online detection system requires minimizing the influence of human parameter selection on the denoising effect. Singular value decomposition (SVD) is often applied to the denoising caused by the system circuit. The selection of the order of singular value denoising is very important to improve the signal-to-noise ratio. However, the selection of parameters mainly depends on empirical debugging and experimental verification. Therefore, this paper proposes a spectral signal denoising algorithm based on singular value reconstruction of signal component frequency. The algorithm firstly reconstructs the single singular value component signal of the original spectral signal. Then, the Fast Fourier Transform (FFT) of each singular value component signal is performed to obtain the frequency value corresponding to the maximum amplitude of each signal. Finally, according to the singular value decreasing mode, the first-order hysteresis difference of the corresponding component signal frequency value is carried out, and the frequency difference spectrum is obtained. The results show that the first peak value of the difference spectrum is the effective order of singular value decomposition denoising. Random noise of different intensity is added to the UV-Visible spectrum signal measured online of a solution containing a variety of metals, and the signal to noise ratio and root mean square error are compared. The results show that the proposed algorithm’s signal-to-noise ratio and root mean square error are 22.05%, 10.88% and 74.28%, 41.29% higher than those of SG filter and wavelet transform respectively. The proposed algorithm is fully data driven, which not only suppresses the noise effect in processing the real UV-Vis spectrum signal, but also effectively filters out the characteristic peak of the light source of the micro spectrometer, so it has a good application prospect in the quantitative analysis of UV-Vis spectrum signal.
Key words：Singular value decomposition; Fast Fourier transform; Spectral denoising; Effective order; Spectral peak
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