1. Extract the data from original 1,000,000 data to reduce the number of data. We select one data from every 1,000 data. So that 1000 data can be obtained for each variable.
2. Export the data sheet from ORIGIN to the text.
3. Import the data sheet to the content of the Matlab.
After that, we can draw the time-frequency using Matlab code as the following algorithm:
1. Import the data sheet to a matrix A.
2. Extract the first column data as variable Time.
3. Extract the second and third column data as input voltage U1 and U2 respectively.
4. Set the sampling frequency is 10,000 and the scale is 128.
5. Calculate the central frequency of wavelets.
6. Change the scale into the frequency.
7. Calculate the continuous wavelet coefficients.
8. Draw the wavelet time-frequency graphs of electrical signals such as U1 and U2.
We obtained the wavelet time-frequency graphs for U1 and U2 as shown in the following Figure:
Figure 1: Wavelet time-frequency for U1
Figure 2: Wavelet time-frequency for U2
From the above two figures, the X-axis represents the time domain and the Y-axis means that the frequency domain, therefore, the signals in time domain are converted into time-frequency domain with using wavelet analysis. The different color in figure represents intensity of the frequency.
As shown in two figures, there are two brilliant bands appearing at around 150 Hz and 4.1 kHz. This results are in agreement with the Fast Fourier Transform. Therefore, the power source period is 6.67 ms and the breakdown period is 0.25 ms respectively.
We will zoom in the time-frequency of U1 and find some characteristic in detail. First, we need to analyze the low frequency at 150 Hz as shown in Figure 3, 4:
Figure 3: Detailed wavelet time-frequency graph at 150 Hz from 0 to 2 ms
Figure 4: Detailed graph of input electrical signal U1
We can compare the last two graphs. When the input signal is increasing, the color around 150 Hz will change from dark blue to light blue, which means that the intensity of the frequency becomes larger. However, when the input voltage is decreasing, the color will be from light blue to dark blue so that the intensity of frequency is smaller. From the above phenomenon, the input voltage affects the intensity of frequency. So the fluctuation of plasma jet is influenced by the undulation of rectified power supply because non-stationary of input signal will affect the intensity of frequency so that output jet is not stationary.
Second, we need to analyze high frequency (4000 Hz) to find another characteristic related to the frequency band as shown in Figure 5, 6.
Figure 5: Detailed wavelet time-frequency graph at 150 Hz from 0.05 to 0.053 s
Figure 6: The corresponding input signal U1
As shown in Figure 5, the frequency band is different from others at 0.05 to 0.053 s. There exists a very narrow frequency band and then band will become wider. So we want to investigate the reason caused it. Why a normal frequency band becomes narrow?
We extract the input electrical signal U1 from 0.05 to 0.053 s to compare with the time-frequency figure. We can observe that the frequency band will be large if the input peak to peak voltage is large enough. In practice, the normal peak to peak voltage is more than 10 V, however, in the last figure, some peak to peak voltages is nearly 5 V. So the narrow frequency band is caused by this kind of voltage whose peak to peak voltage is nearly 5 V. And the large band is due to voltage whose peak to peak value is large.
We need to provide another example to prove this kind of phenomenon as shown in Figure 7, 8.
Figure 7: Detailed wavelet time-frequency graph at 150 Hz from 0.055 to 0.062 s
Figure 8: The corresponding input signal U1
As shown in Figure 5, the frequency band is different from others at 0.05 to 0.053 s. There exists a very narrow frequency band and then band will become wider. So we want to investigate the reason caused it. Why a normal frequency band becomes narrow?
We extract the input electrical signal U1 from 0.05 to 0.053 s to compare with the time-frequency figure. We can observe that the frequency band will be large if the input peak to peak voltage is large enough. In practice, the normal peak to peak voltage is more than 10 V, however, in the last figure, some peak to peak voltages is nearly 5 V. So the narrow frequency band is caused by this kind of voltage whose peak to peak voltage is nearly 5 V. And the large band is due to voltage whose peak to peak value is large.
We need to provide another example to prove this kind of phenomenon as shown in Figure 7, 8.
As shown in Figure 7, there still exists narrow frequency bands from 0.057 to 0.062 s. And then we extract the electrical signal with using the same methods. And we can observe the same phenomenon when we compare the time-frequency and input signal. Also, if the voltage whose peak to peak value is less than 10 V is input, the output narrow band will be appearing. Wider band exists because the peak to peak voltage is more than 10 V.
Therefore, input voltage affects the undulation of the frequency so that it also causes the fluctuation of the Argon-nitrogen double arc plasma jet.
Therefore, input voltage affects the undulation of the frequency so that it also causes the fluctuation of the Argon-nitrogen double arc plasma jet.
