## 6 Discussion  
In this paper, three experimental case studies are conducted for the novel deterministic component cancellation method application in detail. Not only amplitude-frequency characteristics, but also the time-frequency characteristics are analyzed by the S transform. The methods' application in those experimental case studies reveals issues that need to be further discussed and investigated:  
1. The cross-correlation coefficient indicator should be investigated more. The region [0.9, 0.95] is not appropriate for the illustrated cases in this paper. Therefore, there is a need for further study in order to determine the optimal iteration number and a more robust region. 2. The CK indicator takes advantage of when the PIS are more powerful than the other signal components. The case study in Section 3 validates the implanted bearing outer race fault diagnosis, with only bearing fault mode present, and confirms the powerful PIS characteristic of implanted faults. It is confirmed that the CK gives excellent results in determining the optimal iteration number of DC offset cancellation. However, when corrupted by the excess DC offset cancellation operation, the envelope signal analysis will not give a good result because the PIS are also corrupted. For the case study in Section 4, all of the bearing faults are naturally developed. Simultaneously, there are gear chip faults and wear faults. Therefore, the PIS produced by these bearing faults are very weak. In this case, the CK gives a poor result. Theoretically, every DC offset cancellation can suppress one harmonic of the deterministic component of the original signal. For the fixed-axis gearbox, the deterministic component is mainly the HS-IS gear mesh frequency and its harmonics. This is illustrated in Figures 13 and 16 in Section 4. Therefore, it is possible to determine the optimal iteration number by the number of HS-IS gear mesh harmonics. This is very useful for a fixed-axis gearbox. Whereas there is another problem, no  
Figure 27: (**a**) Squared envelope spectrum after the first DC offset cancellation; (**b**) the envelope spectrum of the original signal. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Meshing Frequency**} & \multicolumn{3}{c}{**Rotating Frequency**} & \multicolumn{3}{c}{**Local Damage**} \\ \cline{2-7}  & **Sun** & **Carrier** & **Planet** & **Sun** & **Ring** \\ \hline
267.2586 & 22.3889 & 1.8305 & 4.1759 & 8.3518 & 61.6751 & 5.4916 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Characteristic frequencies (Hz). matter if the squared envelope spectrum after DC offset cancellation or the envelope spectrum of originals signal is used, they are both dominated by the shaft rate and harmonics related to the HS and IS shaft. No information about bearing fault frequencies can be found. Fortunately, the time-frequency contour of the squared envelope signal after DC offset cancellation by the S transform can reveal some information about the bearing fault frequencies. This demonstrates the iterative DC offset cancellation's effectiveness for PIS enhancement. For the implanted bearing outer race fault case study in Section 3, even though both the squared envelope spectrum after DC offset cancellation and the envelope spectrum of the original signal can reveal the bearing fault information effectively, however, the time-frequency contour of the squared envelope signal after DC offset cancellation has good time-frequency characteristics for revealing the bearing fault information, in comparison to the case without DC offset cancellation. 3. Concerning planetary gearbox fault diagnosis, the cross-correlation coefficient has a similar problem as the previous case studies. The CK has the correct assessment for the iteration number for the sun gear fault and the planet gear fault. However, the CK does not take advantage of the ring gear fault, because of the uncertainty for the fault frequency.