Electroencephalography (EEG) signals are commonly used in medical applications for prevention, diagnosis, and detection of neurological diseases. These EEG signals have also been used in designing brain computer interfaces for assistive technologies. For densely placed electrodes and long EEG recordings, a large amount of data needs to be stored, preferably in compressed form. This EEG signal compression is particularly required in an out of the lab environment so that these signals are efficiently transmitted over wired/wireless communication channels. This project propose a novel compression scheme for EEG signals, which exploits the intra channel redundancy using motion compensated temporal filtering (MCTF) and discrete wavelet transform (DWT) based sub-band coding. In the pre-processing stage, multi-frame data is constructed such that each group of picture (GOP) contains information from a single channel of EEG data. This helps in removing the intra-channel redundancy. We apply MCTF on each GOP to exploit temporal redundancy, following which the DWT is applied on temporally decomposed frames to exploit spatial redundancy. Each spatial-temporal decomposed frame is assigned a bit budget for minimum distortion. For this purpose, we assign more bit budget to temporally decomposed low pass frames as compared to high pass frames. Spatial-temporal frames are then encoded at the assigned bit rate by using set partitioning in hierarchical tree (SPIHT) algorithm to create the bit stream. Our experimental results showed 4:5% and 2:4% reduction in distortion at the same data rate for BCI-3 and BCI-4 datasets, respectively. These results improve upon the reduction in data size achieved using state of the art compression methods such as SPIHT and SPIHT with independent component analysis. This project is implemented with MATLAB software.