# Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method +
## 5 Validation of the Proposed Method on Weak Signal Detection  
### Weak Electrical Signal Detection  
To verify the generality of the method SVD-CIM, the weak electrical signal provided by the research group is used for detection and verification, the weak sinusoidal signal is modulated and output. The test system is used to convert it into a digital signal for analysis. Figure 7 is the test system which consists of a signal generator (generate a sine wave), a weak signal amplification analog circuit board (amplify the signal by modulating), a signal acquisition instrument whose type is DH5908N from Donghua (The highest sampling frequency is 128 kHz for each channel, the minimum resolution of the voltage is 5 uV, and powered by a battery. ), a shielding box, and a PC. The sampling frequency is 128 kHz, and the number of sampling points is 1,274,860, the target signal's frequency is 93 Hz. This article uses 4096 points of the signal for verification. Figure 8 is the waveform of the modulated signal. The sine waveform cannot be seen in Figure 8. After the Fast Fourier transformation in Figure 8b, the first two highest amplitudes in the spectrum are 7500 Hz and 15,000 Hz. These high-frequency components have no relationship with the target signal of 93 Hz, it might be related to the means of pre-processing the signal, and 7500 Hz may be related to the carrier frequency. Amplifying the low-frequency band of the spectrum, only a frequency with a peak value of 62.5 Hz is found, so the spectrum cannot be directly used for analysis. Figure 7: The test system. (**a**) The overall test system. (**b**) The analog amplifier circuit board. After performing SVD on the signal, the difference spectrum and CIM are used to select the SCs, respectively. Then, frequency spectrum after FFT is used to compare the difference between the two methods (different spectrum and CIM). The method analysis flowchart is shown in Figure 9. CCES is estimated also to compare with the frequency spectrum. In short, this experiment will compare two methods for choosing SCs and also compare two forms of the spectrogram. Select the first three SCs for signal reconstruction based on the difference spectrum shown in Figure 10a, and choose the SCs whose CIM is lower than the dotted line in Figure 10b for signal reconstruction. Figure 8: The original signal with 93 Hz. (**a**) the waveform of the original signal. (**b**) the frequency spectrum. Figure 9: Single-channel method analysis flowchart. Figure 11 displays the frequency spectrum of the reconstructed signals chosen based on CIM (red line) and differential spectrum (blue line), respectively. For convenience, the method using difference spectrum is called SVD-3 in this section, because it just uses three SCs in this case, and the method using CIM is called SVD-CIM. In the frequency spectrum, method SVD-3 only extracts one frequency component, which corresponds to the spectral line with the highest amplitude in the original frequency spectrum (Figure 8). However, the proposed method SVD-CIM not only extracts the first four high-amplitude signal components corresponding to Figure 8, but also extracts the sideband of 7500 Hz which is related to the characteristic of the target frequency of 93 Hz shown in the partially enlarged view in Figure 11. The Roman numerals 1, 2, 3, and 4 in Figure 11, respectively, represent the first four frequency components of the amplitude in the original signal frequency spectrogram shown in Figure 8.  
As mentioned above, the selection of SCs in SVD adopts a method based on the energy of the differential spectrum, that is, the larger the SV, the greater the energy of the SC. The SV selected by the differential spectrum represents the top amplitude of the original signal frequency spectrum. This is very useful for noise reduction, but it is disadvantageous for the situation where the target signal is completely submerged in the high-frequency, high-amplitude modulation signal.