With an increasing focus on automatic diagnoses of cardiac disease through ECG signals, de-noising techniques that do not introduce artifacts have become necessary. This paper proposes a model based approach for removing high frequency noise from ECG signals. The proposed modeling technique is based on the propagation of the electric waves over the cardiac tissue. The proposed approach models the crucial nodes as a difference between two sigmoid functions. The ECG signal is modeled as the sum of the activity at the SA node, AV node, Bundle branches, Purkenji fibers, and right and left ventricles. The model is adapted to the targeted ECG signal using a nonlinear least squares optimization technique. The proposed filtering approach is applied to randomly selected ECGs from the long-term ST database. A quantitative analysis is performed on simulated ECG signals perturbed with white noise with ST signal to noise ratios ranging from -25 to 5 dB.