Electrocardiogram ECG signal is usually corrupted by several artifacts and these must be removed before diagnosis. This paper therefore presents the design of various FIR filters like Kaiser, Rectangular, Hamming, Hanning, Gaussian and Bartllet window techniques and FIR Equiripple Filter. IIR filters like Butterworth, Chebychev I & II and Elliptic Filters are also explored to remove the artifacts in ECG signal. To verify the usability of designed filters, noisy ECG signal is generated by adding random noise, white noise and 50 Hz interference (hum) to the 100m.mat ECG data sample taken from MIT-BIH database. Signal to noise ratio (SNR) is calculated to compare the performance of different filtering methods using Simulink Model. Results obtained show that FIR Equiripple filter gives a SNR of 7.71 for a 3rd order filter and IIR Elliptic filter has SNR of for first order filter and are therefore recommended