The electrocardiogram (ECG) used for patient monitoring during magnetic resonance imaging (MRI) unfortunately suffers from severe artefacts. These artefacts are due to the special environment of the MRI. Modeling helped in finding solutions for the suppression of these artefacts superimposed on the ECG signal. After we validated the linear and time invariant model for the magnetic field gradient artefact generation, we applied offline and online filters for their suppression. Wiener filtering (offline) helped in generating reference annotations of the ECG beats. In online filtering, the least-mean-square filter suppressed the magnetic field gradient artefacts before the acquired ECG signal was input to the arrhythmia algorithm. Comparing the results of two runs (one run using online filtering and one run without) to our reference annotations, we found an eminent improvement in the arrhythmia module's performance, enabling reliable patient monitoring and MRI synchronization based on the ECG signal.