Atrial Fibrillation (AF) is the most common type of human arrhythmia. Beside its clinical description as absolute arrhythmia, its diagnosis has been assessed for years by visual inspection of the surface electrocardiogram (ECG). Due to the much higher amplitude of the electrical ventricular activity, the analysis of atrial fibrillation requires the previous isolation of the atrial activity component. In this work, an approach to separate atrial and ventricular signal components, decomposing the signal over a redundant multi-component dictionary, is explored. This idea requires a careful dictionary design, taking into account the signal structures and characteristics. Being the dictionary overcomplete, more than one decomposition of a given signal is possible. However, we are interested in sparse solutions. A key point in this work is also, jointly with the dictionary design, to determine the appropriate analysis technique for the best performance of the ECG components separation. Greedy Algorithms, such as Matching Pursuit, or optimization methods, such as Basis Pursuit are studied. To improve our signal separation, the a priori knowledge we have from the ECG signals is also used. Finally, the solution proposed is tested over an ECG database.