## 3 Experimental Results, Verification, and Discussion
Figure 7(d1) illustrates the result of channel 2 being shifted 12 positions forward and then combined with channel 1 to form a signal. It can be clearly seen from the time domain that it is a 200 MHz signal, and its ENOB is calculated to be 4.3445 bits, further verifying the effectiveness of using shift synthesis to recover the original signal. Figure 7(d2) shows the synthesized result of two channel signals being first processed by the PLM and normalization, and then shifted. Based on our calculation, the ENOB reaches 4.3831 bits, which is an improvement compared with Figure 7(d1), but not by much, because the power difference between the signals collected by the two channels is not significant, and the effect of normalization is relatively insignificant at this moment. Figure 7(d3) displays the shift synthesized signal and corresponding fitted signal after applying the PLM and normalization, and it can be found that the processed data match the fitted signal very well. Figure 7(d4) shows the power spectrum information of the normalized shift synthesized signal, which also indicates the top four frequencies and power information with the strongest power. The frequency with the highest power is 200 MHz, followed by 600 MHz, 5.0 GHz, and 4.8 GHz. The power of the main frequency is more than 30.73 dB higher than the other three frequencies, so the nonlinear distortion of the shift synthesized signal is small and can effectively recover the original signal. And it can be found that the average peak noise level of the synthesized signal is also about \(-\)70 dB. The results of the PADC system collecting 21.1 GHz RF signals are depicted in Figure 8. Figure 8a-d illustrate the results of channel 1, channel 2, direct synthesis, and shift corrected synthesis signals, similar to the corresponding relationship presented in Figure 7. According to the Nyquist sampling theorem, for sampling rates of 5.2 GSa/s and 10.4 GSa/s, the 21.1 GHz RF signal will be sub-converted to 300 MHz within the Nyquist bandwidth of 2.6 GHz and 5.2 GHz. Figure 8(a1,b1) display 35 K of raw data collected by two channels of EADCs. Overall, channel 2 exhibits a relatively large peak jitter. Based on our calculations, the ENOBs of channel 1 and channel 2 are 4.8677 and 4.3294 bits, respectively, with average peak-to-peak values of 1582 and 1538, indicating that channel 2 has a slightly lower signal power, albeit the difference is not substantial. Figure 8(a2,b2) present the zoomed-in raw signals collected within the first 15 ns. The solid blue dots represent the collected raw data, and the solid red lines represent the fitted triangular signals. It can be observed that channel 2 experiences greater peak jitter. Figure 8(a3,b3) display the data and corresponding fitted trigonometric signals within the first 15 ns following the PLM and normalization processing, represented by solid blue dots and solid red lines, respectively. It can be discerned that the signal peak jitter has been mitigated, and the original data align well with the fitting function. Based on our calculations, the ENOBs of the two channels are 4.8687 and 4.3575 bits, respectively, surpassing the values of the original data. Furthermore, the enhancement in channel 2's ENOB is more pronounced, further verifying the effectiveness of the PLM and normalization method. Figure 8(a4,b4) illustrate the normalized power spectrum information. The top three frequencies and power information with the strongest power are highlighted in the figures. It can be observed that both channels exhibit the strongest power at 300 MHz, followed by 900 MHz. The power difference at the same frequency in both channels is small for the top two frequencies, but it reaches approximately 6 dB at 600 MHz, indicating that channel 2 experiences a comparatively significant nonlinear distortion.