This study investigates the relationship between sampling frequency and SNR of Electroencephalogram (EEG) signal. The EEG is a standard technique for investigating the electrical activity of brains in different psychological and pathological states. At the time of EEG recording, various artifacts such as muscle activity, eye blinks, eye movements and electrical noise corrupt the EEG signal. Normally, EEG signals fall in the frequency range of DC to 60 Hz and amplitude of 1-5 µv. Ocular artifacts have the similar statistical properties of EEG signals, and often interfere with EEG signal, making the analysis of EEG signals more complex. In this research paper, two different datasets were taken from Physionet data base. The sampling frequency of one dataset is 100Hz and the sampling frequency of another dataset is 250Hz. The research paper attempts to establish the relationship between sampling frequency and SNR of EEG signal. In this paper, the collected EEG signals are normalized and then mixed linearly with the normalized Electrooculography (EOG) signals, resulting in noisy EEG signals. Later soft and hard thresholding techniques were applied for detail coefficients and to estimate the SNR of the denoised EEG signals. This research paper concludes that signals with lower sampling rates provide better SNR than the signals with higher sampling rates. In addition to this, Haar wavelet provided better SNR compared to dB10 and Sym8 wavelets.