## 1 Introduction  
Alzheimer's disease (AD) is a brain disorder that is mainly characterized by a progressive degeneration of neurons in the brain. As the disease progresses, a cortical disconnection occurs, causing a deficit in memory and a decline in other cognitive capabilities [1]. AD-related effects on the patient's brain can be identified with various tools, one option being the electroencephalogram (EEG), which measures the electrical activity of the brain. EEG is a fast and non-invasive method that provides a high temporal resolution. However, it lacks in spatial resolution, meaning that it is not the most precise method for the diagnosis of a brain disorder. Quantitative EEG (qEEG) analysis takes EEG recordings, commonly interpreted by clinicians using visualization tools, one step further, giving the possibility of digitally processing and presenting the signal characteristics in spectral and spatial domains [2]. In a spectral analysis, a given signal is broken down and examined in the frequency domain. This type of analysis is useful when finding differences between patients who are diagnosed with a disorder and healthy individuals, by examining the relevant frequency bands to identify a noticeable change in the activity within a particular frequency band [3]. A very common yet powerful tool used in spectral analysis is the fast Fourier transformation (FFT) [4]. This algorithm can be used to find band-specific differences by calculating the power of each band separately. When conducting a spectral analysis, the power spectral density (PSD) is often used to determine differences in brain activity between frequency bands. Previous studies have shown that when compared to healthy controls (HC), AD patients show an increase of PSD in the theta band and a decrease in the alpha band [3; 5; 6]. In AD diagnosis specifically, a spectral analysis can show discrepancies between AD and other types of dementia, such as vascular dementia (VaD) [1]. However, while these studies suggest that EEG spectral analysis may differentiate AD patients from HC [7], several other studies that have examined the process of AD have concluded that this brain disorder is involved with changes in the distributed networks related to memory [8] and that the changes observed in the frequency bands may not sufficiently reflect this. In addition, it is known that the FFT is not the most adequate tool for non-stationary signals such as the EEG [9; 10]. Moreover, as mentioned above, patients suffering from AD experience a cortical disconnection. It is therefore important to examine various regions of interest (ROIs) that are affected by the disease. Hence, more reliable signal processing methods are required to capture the complexity of this disorder and investigate the processes that underlie the occurring symptoms [11; 12]. An alternative to a spectral analysis is the connectivity analysis; a method which allows one to study the communications between different regions of the brain [12]. Functional connectivity analysis measures the degree of synchronization between two EEG signals; a higher connectivity indicates more effective communication between the examined brain regions [13]. There are several ways of conducting a functional connectivity analysis. For instance, **Coherence analysis** has been used exhaustively in detecting differences between AD patients and HC. Recent studies indicated a decrease in the coherence levels between ROIs for AD [3; 14]. Although coherence has brought some novelty in studies involving AD patients, it is worth mentioning that it solely accounts for linear correlations, thus not considering nonlinear interactions. Nonlinear correlations, on the other hand, can give crucial information in a functional connectivity analysis. A widely used method for this is the **phase synchronization (PS)** analysis. PS looks at the oscillatory activity in two brain regions in terms of their phases [15]. The oscillations are therefore said to be synchronized if their phases are similar.