## 3 Common-Mode Noise and Signal Processing Method for Reconstruction of PC Display
### Reconstruction of PC Display-Image
#### 3.2.2 Signal Processing Method for Reconstruction of PC Displayed Image  
Let \(f\) be a monitor signal and \(g\) be a corresponding common-mode noise. If we can obtain a mathematical expression of the transfer function, the monitor signal \(f\) may be reconstructed analytically from the common-mode noise \(g\). Let \(F\), \(F_{s}\), \(G\), and \(G_{s}\) be the Laplace transforms of the monitor signal \(f\), the step signal \(f_{s}\), the measured response \(g\), and the step response \(g_{s}\), respectively. Then, we have the following relation:  
\[F=\frac{F_{s}}{G_{s}}G. \tag{1}\]  
While the transfer functions \(G_{s}\) and \(F_{s}\) are known, and the function \(G\) is measurable, the function \(F\) can be calculated by using the relation given by Equation (1). Then, the monitor signal \(f\) is calculated by using the inverse Laplace transform of the function \(F\) as:  
\[f=\mathcal{L}^{-1}(F)=\mathcal{L}^{-1}\bigg{(}\frac{F_{s}}{G_{s}}G\bigg{)}. \tag{2}\]  
In this study, we tried to solve the above inverse transferring with numerical analysis by using the actual measured numerical data. Let the reference monitor signal and the measured current of the common-mode noise at an instant \(k\) be \(u(k)\) and \(i(k)\), respectively. The measured current can be written by:  
\[i(k)=I(u(k))+\sum_{i=0}^{k}N_{i}(k) \tag{3}\]  
where \(I(u(k))\) is the noise current level of the reference signal \(u(k)\), and \(N_{i}(k)\) is the value of the beat accompanied with the step change of the reference signal that occurs at instant \(i\). The beat \(N_{i}\) can be written by:  
\[N_{i}=\left\{ \begin{array}{cl}N_{up}&if\ u(i)-u(i-1)>0\\ 0&if\ u(i)-u(i-1)=0\\ N_{down}&if\ u(i)-u(i-1)<0\end{array} \right. \tag{4}\]  
where \(N_{up}\) and \(N_{down}\) are the beats caused by the up-step and the down-step of the reference signal, which are measurable and are shown by Figure 5.  
Figure 5: Step responses of the common-mode noise for: (**a**) up-step, (**b**) down-step. Thus, the reference signal \(u\) can be reconstructed by using Equation (3) as:  
\[u(k)=I^{-1}\Bigg{[}i(k)-\sum_{i=0}^{k}N_{i}(k)\Bigg{]} \tag{5}\]  
where \(I^{-1}\) is the inversion of the noise current level \(I\). Figure 6 shows the sequential frame of the information writing on the monitor. The signal for each line in the monitor started by a horizontal synchronizing signal and moved sequentially. The low signal level continued until reaching the display area. In the display area, the monitor signal exhibited a high or a low level corresponding to the white or the black color. In this study, the dot clock frequency of the monitor was assumed to be known and was used for synchronizing the measured data to the monitor image line by line. The following algorithm was proposed for the signal processing to remove the beats from the measured current. At the beginning, the monitor signal was assumed to be high level (white color) just after entering the display area. The common-mode noise level was also high. The noise level was observed when it decreased continuously--for example, by ten times. The level was judged to change from high to low if it did. Then, the down-step response shown in Figure 5b was subtracted numerically from the original noise waveform. The beginning point for the subtraction corresponded to the instant when the noise level began to decrease in the above judgment. At this instant, the common-mode noise level was low, and the change from low to high level was judged by a continuous increase of the level. The up-step response shown in Figure 5a was subtracted numerically from the above waveform processed for the first down-step. After this, similar processes were repeated. The dot clock frequency was given as a characteristic property of the monitor. The timing when the noise level should have been judged for continuous increase, decrease, or no change could be recognized accurately by an elapsed time from a common-mode pulse wave due to the horizontal synchronizing signal.