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#### Adaptive Filtering Algorithm Based on FFT Amplitude Interval Constraints in Vortex Signal Processing

2016-05-23

Based on the study of the characteristics of vortex signals, the feasibility of FFT in vortex signal processing is analyzed, the concept of FFT amplitude interval constraint is proposed, the frequency of mid-low frequency vortex signals is estimated, and an adaptive filter is designed with Signal processing. 1 Scheme design of signal processing system

1.2 Algorithm Design

The high frequency part can directly use Schmitt trigger to count the frequency. For the traffic below 200Hz, the FFT algorithm is used to analyze the amplitude of each frequency band, and the estimated frequency of the vortex signal is selected according to the amplitude constraint; then this estimated frequency is used as the expected input of the adaptive filter. Adjust the adaptive filter; finally, perform statistical analysis on the filtered signal and display it on the terminal.

2 FFT frequency estimation

2.1 FFT spectrum analysis method

This paper only applies the FFT algorithm from the perspective of frequency estimation. The frequency range used in algorithm analysis is 45Hz ~ 3000Hz (25mm caliber, gas).

2.2 Selection of sampling frequency fs

FFT analysis is only suitable for processing vortex signals at low and medium velocities. This article selects fs = 5fmax = 1000Hz.

2.3 Selection of total sampling time T

In this paper, the total sampling time is 0.5s based on the ± 2Hz error.

2.4 Selecting the number of sampling points using spectrum leakage

Generally, the number of sampling points is N = 512. The use of spectrum leakage can increase the amplitude on both sides of the maximum frequency and prevent the maximum frequency from being divided equally.

2.5 Constraint of effective interval of vortex signal amplitude

Select the theoretical amplitude ± 100% as the effective amplitude interval.

This paper uses an open-loop adaptive filter based on the LMS algorithm, as shown in Figure 6. The vortex signal obtained by sampling the input signal value. The expected signal refers to the estimated signal output by the FFT. The adaptive algorithm designs the system filter based on the input signal and the desired signal. The transfer function of the system can be expressed as (7)

Where N is the number of sample points, n is the order of the FIR filter, x is the input signal, and d is the desired signal. 4 Experimental simulation

In this paper, the sampling frequency is 1000Hz, and 300 sampling points are zero-added to 512 points for FFT analysis. The step size of the adaptive algorithm is 0.008, and the order of the filter will be determined in the following simulation experiments. The signal used is the vortex signal collected online during strong vibration. The display flow of the flow generating device is 49.10 Hz.

4.1 FFT frequency estimation

As shown in Figure 7, the FFT analysis of the vortex signal. From the formula (4), the theoretical amplitude of each frequency point is 0.4f2mV, that is, the upper and lower limits of the vortex signal amplitude are 0.2f2mV and 0.8f2mV, respectively. After the FFT transformation, the point at 48.83 Hz meets the amplitude requirements. Therefore, the estimated frequency of the vortex signal after FFT is 48.83Hz. D (t) = 0.4 · 48.83 · 48.83 · sin (2 · pi · 48.83 · t) mV as the desired signal for adaptive filtering. The results of different filter orders are shown in Figures 8-10.   It can be seen that when n = 16, because the system order is low, noise cannot be completely filtered. N = 32 and n = 64 can meet the filtering requirements. Abandon the instability time caused by the system's uninitialization before 0.05s, and use the Schmitt threshold flip method to calculate the frequency of the obtained waveforms to obtain Table 1. Considering the computational complexity, the order of adaptive filtering is n = 32. At this time, the error is -0.16%.

5 Conclusion

The algorithm strictly controls the calculation amount, the calculation accuracy error is not greater than 0.3%, and the anti-noise capability is strong, which is suitable for the use of industrial field instruments.

Article from Fan Chenyang, Chen Jie, Liu Xiaojia, Huang Shaofeng. Adaptive Filtering Algorithm Based on FFT Amplitude Interval Constraint in Vortex Signal Processing [J] .Industrial Control Computer, 2015,28 (4), 54-56.