This paper analyzes and evaluates various denoising techniques, including Wavelet Transform and Moving Average Filter methods for removing ocular and motion artifacts from EEG signals. The performance of each technique is benchmarked in terms of signal-to-noise ratio (SNR) and normalized mean squared error (NMSE) on available EEG databases, including Bonn and Motion-Artifact Contaminated EEG databases. Simulation results show that the Wavelet Transform using the SURE Shrink algorithm with the hard thresholding rule has the best performance for removing ocular artifacts in intracranial EEG. In contrast, the Wavelet Transform using the universal threshold shrinkage rule with hard thresholding is the preferred method for removing motion artifacts in scalp EEGs. This study is an essential step toward more advanced work to achieve real-time, and low-cost denoising methods for energy-constrained devices.