**2. Preprocessing of cardiac recordings**

Prior to the application of nonlinear indices to surface ECG recordings and intraatrial EGMs, they requires at least the basic preprocessing described in the following subsections.

## **2.1. Surface ECG recording**

The surface ECG recording provides a widely used and non-invasive way to study AF. Some advantages of using the ECG include the ability to record data for a long period of time and the minimal costs and risks involved for the patient, in comparison with invasive procedures [10]. However, because of ECG represents the heart's electrical activity recorded on the thorax's surface, the signal is corrupted by different types of noise, which are picked up by the volume conductor constituting the human body. Thereby, in order to improve later analysis, these recordings need to be preprocessed. Filtering operations have been typically applied to the ECG for the reduction of noise sources, like baseline wandering, high frequency noise and powerline interference [11]. Thus, baseline wander is often removed making use of high-pass filtering (0.5 Hz cut-off frequency), high frequency noise with a low-pass filtering (70 Hz cut-off frequency) and powerline interference with an adaptive notch filtering.

Additionally, the *f* wave analysis from surface ECG recordings is complicated by the simultaneous presence of VA, which is of much higher amplitude. Thereby, the dissociation of atrial and ventricular components is mandatory [12]. Nowadays, several methods to extract the AA signal from surface ECG recordings exist. The most powerful techniques are those that exploit the spatial diversity of the multilead ECG, such as the method that solves the blind source separation problem [3] or the spatiotemporal QRST cancellation strategy [13]. However, the performance of these techniques is seriously reduced when recordings are obtained from Holter systems for paroxysmal AF analysis. The reason is that, generally, Holter systems use no more than two or three leads, which are not enough to exploit the ECG spatial information. For single-lead applications, the most widely used alternative to extract the AA is the averaged beat subtraction (ABS). This method relies on the assumption that the average beat can represent, approximately, each individual beat [12]. Recently, a variety of extensions for this method have been proposed [12, 14].

#### **2.2. Intraatrial EGM**

Nowadays, a variety of intraatrial recording modalities exists, such as bipolar and unipolar recordings from endocardial and epicardial electrodes, optical mapping and noncontact mapping [15]. Although recordings from each one of these modalities have their own characteristics, unipolar recordings are generally characterized by a substantial far-field contamination, such as VA, whereas bipolar recordings contains local atrial activations of the place in which the electrodes are located. Nonetheless, these recordings are also affected by ventricular interference, especially in recording sites closer to the ventricles, even if its effect is less evident than on unipolar EGMs and surface ECG recordings. Thereby, for the VA cancellation both from unipolar and bipolar recordings, an averaged ventricular interference complex, as in ABS, is usually computed and subtracted from each atrial signal [16, 17]. Only remark that the ventricular activations are habitually detected from a surface ECG recording simultaneously acquired for more accuracy.

On the other hand, given that atrial dynamics can be analyzed both from simple EGMs and local atrial period (LAP) series, i.e., the sequence of temporal distances between two consecutive local atrial activations, the appropriate identification of these points is a important task in this context. For this purpose, EGMs are habitually high-pass filtering (40–250 Hz) to remove baseline shifts and high-frequency noise [18]. The filtered signal is then rectified, introducing low-frequency components related to the amplitude of the high-frequency oscillations of the original signal. The modulus of the filtered signal is further low-pass filtered (cut-off at 20 Hz) to extract a waveform proportional to the amplitude of the components of occurring at 40–250 Hz. The atrial activations are then detected by threshold crossing and their occurrence time can be identified by different methods, including the local maximum peak, maximum slope of the atrial depolarization or their barycenter [19].
