It is a fact that contamination of EEG by ocular artifacts reduces the classification accuracy of a brain-computer interface (BCI) and diagnosis of brain diseases in clinical research. Therefore, for BCI and clinical applications, it is very important to remove/reduce these artifacts before EEG signal analysis. Although, EOG-based methods are simple and fast for removing artifacts but their performance, meanwhile, is highly affected by the bidirectional contamination process. Some studies emphasized that the solution to this problem is low-pass filtering EOG signals before using them in artifact removal algorithm but there is still no evidence on the optimal low-pass frequency limits of EOG signals. In this study, we investigated the optimal EOG signal filtering limits using state-of-the-art artifact removal techniques with fifteen artificially contaminated EEG and EOG datasets. In this comprehensive analysis, unfiltered and twelve different low-pass filtering of EOG signals were used with five different algorithms, namely, simple regression, least mean squares, recursive least squares, REGICA, and AIR. Results from statistical testing of time and frequency domain metrics suggested that a low-pass frequency between 6 and 8 Hz could be used as the most optimal filtering frequency of EOG signals, both to maximally overcome/minimize the effect of bidirectional contamination and to achieve good results from artifact removal algorithms. Furthermore, we also used BCI competition IV datasets to show the efficacy of the proposed framework on real EEG signals. The motor-imagery-based BCI achieved statistically significant high-classification accuracies when artifacts from EEG were removed by using 7 Hz low-pass filtering as compared to all other filterings of EOG signals. These results also validated our hypothesis that low-pass filtering should be applied to EOG signals for enhancing the performance of each algorithm before using them for artifact removal process. Moreover, the comparison results indicated that the hybrid algorithms outperformed the performance of single algorithms for both simulated and experimental EEG datasets.