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Removal of noises from ECG (Electrocardiogram) signal is a classical problem. Moreover, nullifying AC and DC noises using the two adaptive algorithms-the LMS and the RLS from the ECG is a new study in biomedical science. In this paper, the four types of AC and DC noises have been implemented according to their basic properties. After that, these noises have been mixed with ECG signal and nullify these noises using the LMS and the RLS algorithms. At the end of this paper, a performance study has been done between these algorithms based on their parameters and also discussed the effect of filter length and the corresponding correlation coefficient. Results indicate that the DC bias noises cannot be handled by the LMS filtering whereas the RLS can handle both types of noises. Also, it is true for both algorithms that the filter length is proportional to MSE (Mean Square Error) rate and it takes more time to converge for both algorithms. Furthermore, most of the cases the RLS has achieved best effective noise cancellation performance although its convergence time is slightly high. But eventually its error has always dipped down below that of the LMS algorithm.