Frequency measurement of LDA signal based on Wavel

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The principle of laser Doppler velocimetry (LDA) is to obtain velocity information by using the Doppler frequency shift of scattered light from moving particles. In the past, the frequency detection of LDA signal can be divided into time domain detection and frequency domain detection. The typical time-domain detection method to return your work to normal is the increasingly reasonable counting space layout method. This method has poor anti noise ability and has very high requirements for Doppler scintillation signals, that is, it requires that only one particle can pass through the measuring volume at any time. The typical frequency domain detection method is FFT. This method lacks time localization property and is not suitable for accurate detection of transient non-stationary signals

wavelet transform has good localization characteristics in both time domain and frequency domain, which is suitable for the detection of transient signals. This method has high resolution in both time domain and frequency domain, and has strong anti noise ability. Ibrahim et al. Pointed out in a paper published in 1994 that the variable resolution characteristics of wavelet transform are not suitable for the detection of LDA signals, and believed that the filter bandwidth of wavelet in the high frequency band is too wide, so that the signal frequency cannot be accurately detected. But it is worth noting that the first thing is that they use dyadic wavelet. In this paper, when Morlet wavelet is used to perform continuous wavelet transform on the signal, the scale parameters change continuously, rather than binary. The simulation results also show that it is feasible to use continuous wavelet transform to measure the frequency of LDA flicker signal

2 characteristics of LDA signal

laser Doppler velocimeter obtains velocity information by relying on the frequency difference (or frequency shift) of light wave between moving particle dispersion light and illumination light. The simplest expression of Doppler frequency shift is:

, where uy is the component of velocity u on the Y axis, κ The angle is the half angle between the incident light and the scattered light vector. As can be seen from the above formula, as long as κ Angle and wavelength λ Given, the relationship between Doppler frequency shift and particle velocity is linear

in laser velocimetry with two beam optical path, the geometric parameters of the measuring body determine the sensitivity coefficient and spatial resolution of the laser velocimeter. When particles pass through the measuring body, the current generated in the photodetector is formed by superposition of two parts. One part is the base signal with Gaussian distribution, which is caused by the change of light intensity of scattered light generated by incident light on particles. The other part is the cosine signal whose envelope is Gaussian distribution, which is the result of the interference of two beams of achromatic light

3 principle of wavelet transform to measure the frequency of LDA signal

Morlet wavelet is a single frequency complex sinusoidal modulated Gaussian wave:

the basic idea of using wavelet to detect the frequency is to carry out wavelet transform on the signal to obtain a three-dimensional time-scale domain, and finally point out that the car interior needs wavelet coefficients with good perceived quality for potential users and car owners. When the frequency f0 of Morlet wavelet generating function is fixed, change the scale factor A. when f0/a is equal to the signal frequency, the modulus of wavelet coefficient reaches the maximum value (equivalent to matched filtering), and the modulus of wavelet coefficient at other points will be less than this value. If you draw a wavelet coefficient diagram, it should be like a mountain peak. The scale corresponding to the "peak" reflects the signal frequency. The relationship between frequency and scale is j=f0/a

4 simulation results

Morlet wavelet is used in the experiment. The frequency f0 of its wavelet generating function is set to 30Hz, and the Doppler frequency range reflecting particle velocity is set to 5mhz~15mhz. According to the relationship between frequency and scale, the range of scale a is set to 1 ×~ seven × Between

4.1 detection of a single LDA scintillation signal

set the fringe number of LDA scintillation signal to 15, the Doppler frequency to 10MHz, the particle arrival time to 1.5ms, and the signal amplitude to 1. The detection result is shown in Figure 1, and figure 1 (a) shows the waveform of LDA flashing signal. Figure 1 (b) shows the time ~ spectrum obtained after wavelet transform of LDA flicker signal, in which the value of a has been converted into the corresponding frequency value (f=f0/a). The ordinate represents the wavelet modulus. It can be seen from the figure that the frequency information of LDA flicker signal and the time information of signal can be obtained by using wavelet transform. Such as signal start time, maximum value time and end time. The result of FFT has only frequency information, but no time information

4.2 detection of two LDA scintillation superimposed signals

Figure 2 shows the detection results of two particles passing through the measuring body at the same time. It is assumed that the characteristics of the particles to be tested are the same as those of the previous simulation experiment particles. Then an interfering particle is given. The fringe number of LDA scintillation signal is set to 14, the Doppler frequency is 11mhz, the particle arrival time is 1.56ms, and the signal amplitude is 0.7. Figure 2 (a) shows the signal waveform of the superposition of two particles, and Figure 2 (b) shows the time-frequency diagram of the superposition signal. The time and frequency of arrival of interfering particles are clearly shown in the figure. The arrival time of particles cannot be detected by FFT. If two particles pass through the path of the measuring body, the angle is exactly the same, that is, the Doppler frequency is the same, but the arrival time is different. Then one particle or two particles cannot be detected in FFT. However, it is different in the wavelet domain. As shown in Figure 2 (b), the characteristics of the two particles will be clearly separated. Simulation experiments show that the same is true

5 conclusion

the traditional frequency domain analysis method of LDA is based on Fourier series theory and based on trigonometric function, which is lack of time-domain localization property. The analysis method based on wavelet transform in this paper takes wavelet as the base of function expansion, which has good localization characteristics in both time domain and frequency domain, and is more suitable for the detection and time-frequency analysis of time-varying non-stationary signals. The wavelet domain analysis method proposed in this paper makes use of the time-frequency analysis characteristics of wavelet to realize the detection of LDA flicker signal. Compared with FFT method, it can be seen that this method is conducive to signal location and strong interference ability, especially for multi particle detection

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