Study on digital filter to filter out power frequency and harmonic interference in electronic measurement system
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Abstract: In electronic measurement, power frequency is one of the main sources of noise interference. If it is not filtered out, it will greatly affect the measurement accuracy. The traditional analog circuit filter cannot compare with the digital filter in terms of accuracy; in addition, the analog circuit design of multi-stopband filters is even more impossible to achieve. This design uses the FIR (Finite Impulse Response) digital filtering principle to design a three-stopband digital filter with stopband ranges of 48 ~ 52 Hz, 98 ~ 102 Hz, and 148 ~ 152 Hz. Simulation experiments have shown that it will attenuate the power frequency 50 Hz and its second harmonic and third harmonic interference in the electronic measurement system by 30 dB. The denoised signal is analyzed to greatly improve the accuracy of the test system. The whole process is divided into mathematical modeling of multi-stopband filters and implementation of filtering algorithms, and the effects of changes in different window functions and orders on filtering performance are analyzed and compared.
Keywords: power frequency noise suppression; FIR multi-stopband digital filtering; filter resolution; mathematical modeling Digital Filter Application for Squelch on Industrial
FrequencyNoise and Its Harmonic Waves Interference WEN Weijun1，WANG Lei2，SUN Haiying1 (1.Information College, Qingdao University of Science and Technology,
Qingdao, 2 66042, China;
2. Automatic Engineering Company, Qingdao Drainage Department,
Qingdao, 266021, China) Abstract： Industrial frequency and its harmonious waves are one of the main interferences in electronic measurement,which will cause severe influence on test accuracyDigital filter is better than analog filter at resolution,furthermore multiband stop filter design is unrealizable for analog filter design method This paper designs an FIR(Finite Impulse Response) multi band stop digital filter to reject the noise of 50 Hz and its harmonic waves from power network,whose stop bands are respectively as 48~52 Hz,98 ~ 102 Hz and 148 ~ 152 Hz?Simulation results prove that the noise can be depressed to 30 dB?To analyze the filtered signal can improve accuracy of the test system? The whole course includes two parts,which are filter mathematical modeling and filter algorithm implementatio n on worksite dada
Keywords： industrial frequency noise squelch;FIR band stop digital filter;filter resolut ion;mathematical modeling The main noise source in the electronic measurement system is the 50 Hz power frequency and its harmonic interference from the power grid, mainly the second and third harmonics, while higher harmonics can be ignored due to their small spectral components. If their noise pollution is not removed, it will inevitably affect the measurement accuracy. Traditional analog filters cannot compare with digital filters in terms of accuracy, especially in the design of multi-stopband and multi-passband filters, analog filters are even more powerless. Based on the characteristics of the noise source, this paper uses digital signal processing theory to design a high-order multi-stopband and multi-passband filter, and uses numerical calculation methods to achieve the purpose of suppressing noise, extracting signals and facilitating application. 1FIR multi-stopband and multi-passband digital filter design
1.1 Spectral characteristics and time domain model of ideal three-stopband FIR digital filter system
If a three-stopband digital filter has a frequency characteristic of H(e jω ), its passband is 500)this.style.width=500;" border=0>
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It can also be seen from Figure 2 that the filter has a linear phase, which is one of the advantages of the FIR filter. 2 Time domain convolution calculation filter output
2.1 Acquisition of signal x(n) mixed with noise
The useful signal is s(n), which is polluted by power frequency noise and its harmonics. Since the high-order harmonics occupy a small part of the spectrum and are negligible, only the interference of the second harmonic of 100 Hz and the third harmonic of 150 Hz is considered, so the designed filter has only 3 stop bands. In fact, if the interference of the 4th and 5th harmonics is also considered, the stop band should be increased to 5. The design method is similar, as long as the mathematical model is modified. In order to facilitate the verification of the performance of the filter, it is assumed that the useful signal s(n) is a sinusoidal signal with a frequency of 75 Hz, and the time domain and frequency domain diagrams of the signal x(n) are shown in Figure 3.  500)this.style.width=500;" border=0> ?
2.2 Time Domain Convolution
Assume that the length of x(n) is N 1 points and the length of filter h N (n) is N 2 , then the convolution output y(n) should be N 1 +N 2 -1 points, but only the N 1 -N 2 points of y(N 2 -1) ~ y(N 1 -1) are the real results [1]. The time domain and frequency domain of y(n) are shown in Figure 4.  500)this.style.width=500;" border=0>
3 Effect of changing parameters on filtering effect
3.1 Effect of order change on filtering performance
When the sampling frequency is kept constant at fs = 1 500Hz and the window function is kept constant, the filtering effect will also change significantly if the order of the filter is changed. The filtering effect of the filter with order M = 399, 499, and 599 is compared as shown in Figure 5. It can be concluded that as the order N increases, N/fs = ΔT becomes smaller, so the better the resolution Δf = 1/ΔT of the filter [1], the better the filtering effect, which is consistent with the experimental results.  500)this.style.width=500;" border=0>
3.2 Effect of different window functions on filtering performance
To achieve good filtering effect, not only a higher filtering order is required, but also a suitable window function needs to be selected [2]. Below, the effect of different window functions on filtering effect is compared when the order is 399 and the sampling frequency is 1500 Hz, as shown in Figure 6.  500)this.style.width=500;" border=0>
After the above comparison, it can be seen that the filtering effect of the Hanning window and the Hamming window is better than that of the Blackman window. This is because the main lobe width of the Hanning window and the Hamming window is Bo = 8π/N, while the main lobe width of the Blackman window is Bo = 12π/N. It can be seen that the main lobe width plays a major role in the influence of the filtering effect. The narrower the main lobe, the better the filtering effect [1]. As the order M increases, the main lobe width becomes narrower, and the influence of the window function becomes smaller and smaller. Therefore, when the order is relatively small, the window function has a great influence on the filtering effect. 4 Conclusion
Since the bandwidth between power frequency noise and its harmonics is only 50 Hz, in order to better suppress this interference, the transition band between each stop band is required to be relatively narrow. The main lobe width of the window function affects the transition band of the filter [3]. Since the main lobe width is the inverse of the order [1], the order of the filter should be above 1000. In order to improve the convolution speed, the FFT algorithm can be used to achieve real-time filtering output. ［1］Hu Guangshu. Digital Signal Processing Theory, Algorithms and Practice［M］. Beijing: Tsinghua University Press, 1997.［
2］Zheng Nanning. Digital Signal Processing［M］. Xi'an: Xi'an Jiaotong University Press, 1991.
［3］Zhou Liqing, Quan Ziyi. Digital Signal Processing［M］. Beijing: Beijing University of Posts and Telecommunications Press, 1994.
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