**2. Atrial activity extraction**

This section describes the most widely used methods to separate atrial from ventricular activities, both on surface and invasive recordings, grouped by they core way of operation. Mathematical notation or equations have been avoided in the interest of readability. Anyway, the reader could find detailed explanations in the corresponding references. Firstly, the methods based on the generation of an average beat, able to represent approximately each individual beat, are detailed. Within these methods, the main idea is to subtract the average beat from every single beat. Next, other group of methods take profit of physiological observations such as atrial and ventricular activities being uncoupled and originated from independent electrical sources. This fact allows the application of signal separation methods to dissociate atrial from ventricular activities, that will be addressed later.

## **2.1. Average Beat Subtraction methods**

The average beat subtraction (ABS) based method was firstly presented by Slocum et al. [3] and still remains as the most widely used on the surface ECG [12, 13]. The ABS methodology takes advantage of the lack of a fixed relationship between atrial and ventricular activities and the consistent morphology of the QRST complexes [3]. In this method, fiducial points from ventricular complexes are detected and aligned [14]. Next, an average beat is generated where the window length is determined by the minimum or mean R–R interval. The window was aligned such that 30% of it preceded the fiducial point and 70% followed it [15]. A template of average beats was constructed and subtracted from the original signal, resulting in the atrial activity with subtracted ventricular activity.

The use of an adaptive template in conjunction with the correct alignment of every QRS complex, both in time and space, has proven to be very effective through the spatiotemporal QRST cancellation [16]. Since ABS is performed in individual leads, it becomes sensitive to alterations in the electrical axis, which are manifested as large QRS-related residuals. However, the effect of such alterations can be suppressed by using the spatiotemporal QRST cancellation in which the average beats of adjacent leads are mathematically combined with

2 Atrial Fibrillation

time-frequency analysis or spectral modeling.

electrical cardioversion [11].

**2. Atrial activity extraction**

**2.1. Average Beat Subtraction methods**

in the atrial activity with subtracted ventricular activity.

AF recordings with low DAF are more likely to terminate spontaneously and to respond better to antiarrhythmic drugs or cardioversion, whereas high DAF is more often associated with persistence to therapy [6]. The likelihood of successful pharmacological cardioversion is higher when the DAF is below 6 Hz [7]. Moreover, the risk of early AF recurrence is higher for patients with higher DAF [8] and, therefore, the DAF may be taken into consideration when selecting candidates for cardioversion. Section § 3 will provide to the reader basic concepts and recent advances in DAF estimation, as well as more elaborated techniques like

On the other hand, organization deals with strategies to quantify the repetitiveness of the AF signal pattern, thus providing very useful clinical information on the arrhythmia state. This relevant concept will be addressed in Section § 4, where the most important methods will be described [9, 10]. AF organization has demonstrated its clinical usefulness because indices of organization have been related to the electrophysiological mechanisms sustaining AF, or may be useful in the evaluation of strategies for AF treatment, such as catheter ablation or

This section describes the most widely used methods to separate atrial from ventricular activities, both on surface and invasive recordings, grouped by they core way of operation. Mathematical notation or equations have been avoided in the interest of readability. Anyway, the reader could find detailed explanations in the corresponding references. Firstly, the methods based on the generation of an average beat, able to represent approximately each individual beat, are detailed. Within these methods, the main idea is to subtract the average beat from every single beat. Next, other group of methods take profit of physiological observations such as atrial and ventricular activities being uncoupled and originated from independent electrical sources. This fact allows the application of signal separation methods

The average beat subtraction (ABS) based method was firstly presented by Slocum et al. [3] and still remains as the most widely used on the surface ECG [12, 13]. The ABS methodology takes advantage of the lack of a fixed relationship between atrial and ventricular activities and the consistent morphology of the QRST complexes [3]. In this method, fiducial points from ventricular complexes are detected and aligned [14]. Next, an average beat is generated where the window length is determined by the minimum or mean R–R interval. The window was aligned such that 30% of it preceded the fiducial point and 70% followed it [15]. A template of average beats was constructed and subtracted from the original signal, resulting

The use of an adaptive template in conjunction with the correct alignment of every QRS complex, both in time and space, has proven to be very effective through the spatiotemporal QRST cancellation [16]. Since ABS is performed in individual leads, it becomes sensitive to alterations in the electrical axis, which are manifested as large QRS-related residuals. However, the effect of such alterations can be suppressed by using the spatiotemporal QRST cancellation in which the average beats of adjacent leads are mathematically combined with

to dissociate atrial from ventricular activities, that will be addressed later.

**Figure 1.** Relevant time instants used by the ASVC algorithm. The points *si* and *ei* are the start and end points of the *i*-th QRST complex which is represented by **x***i*, respectively. The points *osi* and *oei* define the zones, at the beginning and the end of the *i*-th QRST complex, that will be processed to avoid sudden transitions after ventricular cancellation [13].

the average beat of the analyzed lead in order to optimize cancellation [16]. Other authors have proposed the idea of processing separately the QRS complex and the T wave [17]. This is because the depolarization waveform changes notably as a function of the heart rate, whereas the repolarization waveform remains almost unchanged.

Finally, the most recently ABS method is based on adaptive singular value cancellation (ASVC) of the ventricular activity [13]. Given that the ECG signal presents a high degree of temporal redundancy which could be exploited for ventricular activity cancellation, the ASVC method detected all the R waves making use of the Pan and Tompkins technique [14]. Next, the starting and ending points of each QRS complex were detected and the complexes were aligned using their R peak timing. Figure 1 depicts the fiducial points and relevant time instants described herein. Once all the beats were temporally aligned, their eigenvector sequence was obtained by singular value decomposition (SVD). In this way, the highest variance provided the eigenvector considered as the representative ventricular activity [13]. Thereby, this activity was used as the primary cancellation template. Next the template was adapted to each QRST width and height and was temporally aligned with each R peak in the ECG. Finally, the customized template for each beat was subtracted from every QRST complex and the atrial activity estimation inside the complex was obtained. This SVD–based method provided a more accurate ventricular activity representation adapted to each individual beat and, as a consequence, a higher quality AA extraction in a wide variety of AF recordings [13].

As an illustration on how the ABS-based methods can behave, Figure 2 plots the comparison between the simple ABS method introduced in [3] and the ASVC method presented in [13]. As can be observed, ventricular residua use to be present in the extracted AA, specially for the simple ABS method in (c). In fact, this is the main reason justifying the permanent optimization of atrial activity extraction methods during last years.

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#1

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**Figure 3.** Input and result of the BSS separation process applied to an ECG of atrial fibrillation. (a) 12-lead ECG segment from a patient in AF. The multi-lead information will be used by BSS to yield a unified atrial activity. (b) Estimated sources obtained

via BSS and reordered from lower to higher kurtosis value. The unified atrial activity is contained in source #1 [4].

I

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**Figure 2.** Example of a real ECG segment in AF with irregular QRST shape and the illustration on how the ABS-based method are able to cancel out ventricular activity. (a) ECG ready for ventricular activity cancellation. (b) Atrial activity signal provided by ASVC [13]. (c) Atrial activity signal provided by ABS [3].

#### **2.2. Signal separation methods**

Other recently proposed alternative consist of applying signal separation algorithms, which are able to use the multi-lead information provided by the ECG to obtain a unified atrial activity. They can be based on principal component analysis (PCA) [18] or blind source separation (BSS) [4]. These methodologies have been compared in a joint study proving their coincident results in the estimation of AF spectra on the surface ECG [19]. One common drawback to the ABS-based methods is that they are mainly thought to be applied over single lead ECGs. In other words, the application of ABS cancellation techniques to different ECG leads would involve the obtention of an equal number of different atrial activities as well. Consequently, they do not make use of the information included in every lead in an unified way. On the contrary, BSS techniques perform a multi-lead statistical analysis by exploiting the spatial diversity that multiple spatially-separated electrodes may introduce [4, 20].

The blind source separation consists in recovering a set of source signals from the observation of linear mixtures of the sources [21]. The term *blind* emphasizes that nothing is known about the source signals or the mixing structure, the only hypothesis being the source mutual independence [22]. To achieve the source separation, a linear transformation is sought such that the components of the output signal vector become statistically independent, thus representing an estimate of the sources except for (perhaps) scaling and permutation, which are considered as admissible indeterminacies [22]. Some authors have proposed the use of PCA to solve the mixing model between atrial and ventricular activity in AF [23]. However, it is important to remark that the success of PCA relies heavily on the orthogonality of the sources. But, in general, there is no reason why bioelectrical sources of the heart should be spatially orthogonal to one another in the ECG. This orthogonality condition can only be forced through appropriate electrode placement, as previously emphasized in the context of the fetal ECG extraction problem [24] and the cancellation of artifacts in the electroencephalogram [25].

4 Atrial Fibrillation

**Figure 2.** Example of a real ECG segment in AF with irregular QRST shape and the illustration on how the ABS-based method are able to cancel out ventricular activity. (a) ECG ready for ventricular activity cancellation. (b) Atrial activity signal provided by

Other recently proposed alternative consist of applying signal separation algorithms, which are able to use the multi-lead information provided by the ECG to obtain a unified atrial activity. They can be based on principal component analysis (PCA) [18] or blind source separation (BSS) [4]. These methodologies have been compared in a joint study proving their coincident results in the estimation of AF spectra on the surface ECG [19]. One common drawback to the ABS-based methods is that they are mainly thought to be applied over single lead ECGs. In other words, the application of ABS cancellation techniques to different ECG leads would involve the obtention of an equal number of different atrial activities as well. Consequently, they do not make use of the information included in every lead in an unified way. On the contrary, BSS techniques perform a multi-lead statistical analysis by exploiting the spatial diversity that multiple spatially-separated electrodes may introduce [4, 20].

The blind source separation consists in recovering a set of source signals from the observation of linear mixtures of the sources [21]. The term *blind* emphasizes that nothing is known about the source signals or the mixing structure, the only hypothesis being the source mutual independence [22]. To achieve the source separation, a linear transformation is sought such that the components of the output signal vector become statistically independent, thus representing an estimate of the sources except for (perhaps) scaling and permutation, which are considered as admissible indeterminacies [22]. Some authors have proposed the use of PCA to solve the mixing model between atrial and ventricular activity in AF [23]. However, it is important to remark that the success of PCA relies heavily on the orthogonality of the sources. But, in general, there is no reason why bioelectrical sources of the heart should be spatially orthogonal to one another in the ECG. This orthogonality condition can only be forced through appropriate electrode placement, as previously emphasized in the context of the fetal ECG extraction problem [24] and the cancellation of artifacts in the

ASVC [13]. (c) Atrial activity signal provided by ABS [3].

**2.2. Signal separation methods**

electroencephalogram [25].

**Figure 3.** Input and result of the BSS separation process applied to an ECG of atrial fibrillation. (a) 12-lead ECG segment from a patient in AF. The multi-lead information will be used by BSS to yield a unified atrial activity. (b) Estimated sources obtained via BSS and reordered from lower to higher kurtosis value. The unified atrial activity is contained in source #1 [4].

When BSS is applied to an ECG in AF, a set of different sources can be observed as illustrated in Figure 3. Consequently a crucial step in BSS-based atrial activity extraction is to identify the sources(s) which contains atrial activity. The first algorithm proposed for this purpose made use of a kurtosis-based reordering of the components, relying on the assumption that sub-Gaussian sources are associated with atrial activity, approximately Gaussian ones with various types of noise and artifacts, whereas super-Gaussian sources are associated with ventricular activity [4]. Since information on kurtosis alone is insufficient for accurate identification of the atrial component, kurtosis reordering was combined with power spectral analysis of the sub-Gaussian components to detect when a dominant spectral peak, reflecting atrial rate, was present or not. It is commonly accepted that atrial rate is reflected by a peak whose frequency is confined to the interval 3–9 Hz [4]. In this respect Figure 4 shows the power spectral density associated to the separated sources with lower kurtosis in Figure 3. As can be appreciated, source #1 is the one representing the typical spectrum of an atrial activity.

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**Figure 5.** Block diagram of the BSS method, implemented by independent component analysis (ICA), and SOBI for atrial activity extraction in multi-lead ECGs of AF. It can be observed that components whose kurtosis exceed 1.5 are excluded from the SOBI

atrial implantable cardioverter-defibrillators [28]. Within this context, ABS (or a similar methodology) has been applied to the AEG in order to discriminate sinus rhythm from AF [15], to measure AF organization [9] and synchronization [29] and to monitor the effects

However, ABS tends to distort the resulting atrial signal when the AEG under analysis corresponds to a well organized AF, as Figure 6 shows. Observe in Fig. 6.a that the atrial rhythm is well organized and uncoupled with the ventricular rhythm. The AEG shows ventricular depolarization contamination and the remaining three signals are the resultant atrial activity after applying ventricular reduction with the corresponding algorithm. Observe how ABS can modify the atrial waveform within the atrial segments. In contrast, Fig. 6.b shows a disorganized AF episode. In this case, thanks to the irregularity of the atrial signal, ABS performs better, preserving the atrial waveform and reducing ventricular peaks. Because of the aforementioned problems with ABS, alternative methods have been introduced in the literature [31]. Firstly, adaptive ventricular cancellation (AVC) can be considered. This method is based on an adaptive filter that operates on the reference channel to produce an estimate of the interference, which is then subtracted from the main channel [32]. In this case the main channel was the recorded AEG containing both atrial and ventricular components. On the other hand, the reference channel was lead II from the standard surface ECG. The motivation to select this lead was based on the large ventricular amplitude that can be observed on it, and the precise time alignment existing between the QRS complex of lead II and the AEG [12, 33]. The resulting atrial activity provided by the

AVC method can be observed in Figure 6 for two different types of AF recordings.

The last approach introduced to deal with AA extraction from the AEG has been based also in BSS through the use of independent component analysis (ICA) [31]. This is because in the context of AF patients, atrial and ventricular activities can be considered as decoupled electrical processes that appear mixed at the electrode output [4]. Therefore, it should be possible to dissociate atrial from ventricular activity in one AEG lead by using the proper reference signal which, in this case, has been the surface standard lead II by the same reasons as with AVC. In this case, the dimension is 2 × 2 where the observations are composed of the AEG and lead II, and the sources are the atrial and ventricular components to be dissociated. The FastICA algorithm was preferred to perform the ICA process due to its fast convergence and robust performance, previously demonstrated in a variety of different applications [34].

of ablation procedures and antiarrhythmic drugs [30].

stage [20].

**Figure 4.** Power spectral densities from several BSS-estimated sources of Fig. 3. After kurtosis-based reordering only five sources have subgaussian kurtosis, and the one with lowest kurtosis (source #1) presents a power spectral density typically associated with the atrial activity in AF episodes [4].

Another approach to atrial component identification was later presented in [20], where kurtosis reordering and spectral analysis are supplemented with another technique with which ventricular components are excluded from further processing and only components with possible atrial activity are retained. Since the kurtosis of the ventricular components is usually very high, they can be excluded with a simple threshold test. It was found that a threshold of about 1.5 retained components with atrial activity, but excluded components with QRS complexes. The block diagram of this technique is represented in Figure 5.

The nonventricular components, i.e., atrial activity, noise, and artifacts, with kurtosis close to zero, are separated using second-order blind identification (SOBI). This technique aims at separating a mixture of uncorrelated sources with different spectral content through second-order statistical analysis which also takes into consideration the source temporal information [20].

#### **2.3. Specific methods for invasive recordings**

In the same way as with surface ECG recordings, other relevant point of view to understand the pathophysiological mechanisms of AF is the analysis and interpretation of atrial electrograms (AEG), which are recordings obtained on the atrial surface. More precise and successful therapies can be developed through this analysis, like guided radio-frequency ablation [26], analysis of antiarrhythmic drug effects [27] or performance improvement of

6 Atrial Fibrillation

activity.

Normalized Amplitude

When BSS is applied to an ECG in AF, a set of different sources can be observed as illustrated in Figure 3. Consequently a crucial step in BSS-based atrial activity extraction is to identify the sources(s) which contains atrial activity. The first algorithm proposed for this purpose made use of a kurtosis-based reordering of the components, relying on the assumption that sub-Gaussian sources are associated with atrial activity, approximately Gaussian ones with various types of noise and artifacts, whereas super-Gaussian sources are associated with ventricular activity [4]. Since information on kurtosis alone is insufficient for accurate identification of the atrial component, kurtosis reordering was combined with power spectral analysis of the sub-Gaussian components to detect when a dominant spectral peak, reflecting atrial rate, was present or not. It is commonly accepted that atrial rate is reflected by a peak whose frequency is confined to the interval 3–9 Hz [4]. In this respect Figure 4 shows the power spectral density associated to the separated sources with lower kurtosis in Figure 3. As can be appreciated, source #1 is the one representing the typical spectrum of an atrial

Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) <sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>0</sup>

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>0</sup>

**Figure 4.** Power spectral densities from several BSS-estimated sources of Fig. 3. After kurtosis-based reordering only five sources have subgaussian kurtosis, and the one with lowest kurtosis (source #1) presents a power spectral density typically

Another approach to atrial component identification was later presented in [20], where kurtosis reordering and spectral analysis are supplemented with another technique with which ventricular components are excluded from further processing and only components with possible atrial activity are retained. Since the kurtosis of the ventricular components is usually very high, they can be excluded with a simple threshold test. It was found that a threshold of about 1.5 retained components with atrial activity, but excluded components with QRS complexes. The block diagram of this technique is represented in Figure 5.

The nonventricular components, i.e., atrial activity, noise, and artifacts, with kurtosis close to zero, are separated using second-order blind identification (SOBI). This technique aims at separating a mixture of uncorrelated sources with different spectral content through second-order statistical analysis which also takes into consideration the source temporal

In the same way as with surface ECG recordings, other relevant point of view to understand the pathophysiological mechanisms of AF is the analysis and interpretation of atrial electrograms (AEG), which are recordings obtained on the atrial surface. More precise and successful therapies can be developed through this analysis, like guided radio-frequency ablation [26], analysis of antiarrhythmic drug effects [27] or performance improvement of

k

2

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**2.3. Specific methods for invasive recordings**

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10

associated with the atrial activity in AF episodes [4].

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information [20].

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**Figure 5.** Block diagram of the BSS method, implemented by independent component analysis (ICA), and SOBI for atrial activity extraction in multi-lead ECGs of AF. It can be observed that components whose kurtosis exceed 1.5 are excluded from the SOBI stage [20].

atrial implantable cardioverter-defibrillators [28]. Within this context, ABS (or a similar methodology) has been applied to the AEG in order to discriminate sinus rhythm from AF [15], to measure AF organization [9] and synchronization [29] and to monitor the effects of ablation procedures and antiarrhythmic drugs [30].

However, ABS tends to distort the resulting atrial signal when the AEG under analysis corresponds to a well organized AF, as Figure 6 shows. Observe in Fig. 6.a that the atrial rhythm is well organized and uncoupled with the ventricular rhythm. The AEG shows ventricular depolarization contamination and the remaining three signals are the resultant atrial activity after applying ventricular reduction with the corresponding algorithm. Observe how ABS can modify the atrial waveform within the atrial segments. In contrast, Fig. 6.b shows a disorganized AF episode. In this case, thanks to the irregularity of the atrial signal, ABS performs better, preserving the atrial waveform and reducing ventricular peaks.

Because of the aforementioned problems with ABS, alternative methods have been introduced in the literature [31]. Firstly, adaptive ventricular cancellation (AVC) can be considered. This method is based on an adaptive filter that operates on the reference channel to produce an estimate of the interference, which is then subtracted from the main channel [32]. In this case the main channel was the recorded AEG containing both atrial and ventricular components. On the other hand, the reference channel was lead II from the standard surface ECG. The motivation to select this lead was based on the large ventricular amplitude that can be observed on it, and the precise time alignment existing between the QRS complex of lead II and the AEG [12, 33]. The resulting atrial activity provided by the AVC method can be observed in Figure 6 for two different types of AF recordings.

The last approach introduced to deal with AA extraction from the AEG has been based also in BSS through the use of independent component analysis (ICA) [31]. This is because in the context of AF patients, atrial and ventricular activities can be considered as decoupled electrical processes that appear mixed at the electrode output [4]. Therefore, it should be possible to dissociate atrial from ventricular activity in one AEG lead by using the proper reference signal which, in this case, has been the surface standard lead II by the same reasons as with AVC. In this case, the dimension is 2 × 2 where the observations are composed of the AEG and lead II, and the sources are the atrial and ventricular components to be dissociated. The FastICA algorithm was preferred to perform the ICA process due to its fast convergence and robust performance, previously demonstrated in a variety of different applications [34].

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spectral profile or the spectral modeling have proven to be efficient techniques that will be

The computation of power spectral analysis on the atrial activity signal is the most common approach to determine the DAF [7]. Basically, the technique consist of locating the largest spectral peak within the power spectrum. The spectrum is usually defined as the discrete Fourier transform of the autocorrelation function of the signal. In this case, the signal is the atrial activity which is divided into shorter, overlapping segments, where each segment is subjected to proper windowing, e.g., using commonly the Welch's method [35]. Finally, the desired power spectrum is obtained by averaging the power spectra of the respective

Primarily there exist two ways to compute the power spectral density of a discrete signal. First, estimate its autocorrelation function and then take its Fourier transform. Second, compute the Fourier transform of the signal and, next, square its magnitude to obtain the periodogram. Normally, the second way is the most commonly applied because of the great

Depending on prior information about the signal, spectral estimation can be divided into two categories: nonparametric and parametric approaches. Nonparametric approaches explicitly estimate the autocorrelation function or the power spectral density of the process without any prior information. On the other hand, parametric approaches assume that the underlying random process has a certain structure, for example, an autoregressive (AR) model, which can be described using a small number of parameters and estimate the parameters of the model [37]. A widely used nonparametric estimation approach is the periodogram, which is based on the fast Fourier transform (FFT). A common parametric technique is maximum entropy spectral estimation, which involves fitting the observed signal to an AR model [36]. The raw periodogram is not a statistically stable spectral estimate since there is not much averaging on its computation. In fact, the periodogram is computed from a finite-length observed sequence that is sharply truncated. This sharp truncation effectively spreads the original signal spectrum into other frequencies, which is called spectral leakage [37]. The spectral leakage problem can be reduced by multiplying the finite sequence by a windowing function before the FFT computation, which reduces the sequence values gradually rather than abruptly. In order to reduce the periodogram variance, averaging can be applied. This modified algorithm is called Welch's method, which is the most widely used in nonparametric spectral estimation [35]. In order to increase the number of segments being averaged in a finite-length sequence, the sequence can be segmented with overlap; for example, 50% overlap can duplicate the number of segments of the same length [35]. Segment length can be considered as the most important parameter in AF spectral analysis since it determines the estimation accuracy of the DAF by restricting spectral resolution. It is advisable that the segment length is chosen to be at least a few seconds so as to produce an

With respect to the surface ECG lead selection for AF power spectral analysis, this lead use to be V1. This is because lead V1 contains the fibrillatory waves with largest amplitude and, therefore, the associated DAF peak will be the largest in this lead [12]. As an example of

computational efficiency of the fast Fourier transform algorithm [36].

acceptable variance of the power spectrum [1, 2].

detailed by the end of this section.

**3.1. Power spectral analysis**

segments.

**Figure 6.** (a) From top to bottom, Lead II of an organized AF ECG shown for reference, the corresponding epicardial atrial electrogram (AEG), result of ventricular reduction with average beat subtraction (ABS), adaptive ventricular cancellation (AVC) and independent component analysis (ICA). (b) This panel plots the same information as panel (a) for a disorganized AF ECG. Note how ABS does not distort the resulting signal in this latter case [31].

The results provided by ICA in separating the atrial activity from ventricular contamination in AEGs are considered as better than those provided by ABS or AVC regarding how the atrial waveforms are preserved and the amount of ventricular residue removed [31], see Figure 6.

#### **3. Frequency analysis of AF**

When an atrial activity signal is available after QRST cancellation, the power spectral analysis door can be opened for the purpose of locating the dominant atrial frequency. This will be the first aspect to be addressed in this section. However, it is well known that the fibrillatory waves present time-dependent properties that may be blurred through a basic spectral analysis. As a consequence, when more detailed information and robust spectral estimation are needed, time-frequency analysis may be the way to go. In this respect, concepts like the spectral profile or the spectral modeling have proven to be efficient techniques that will be detailed by the end of this section.
