# Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals
## 1 Introduction  
Sleep is one of the basic physiological needs, and an important part of life. A typical human spends one-third of his lifetime sleeping. Lack of sleep may cause health issues, influence mood, and interfere with cognitive performance [1; 2]. Examination of sleep is usually performed with the aid of polysomnography (PSG). PSG is used to examine multiple parameters that may be useful in the diagnosis of sleep disorders, or may be analyzed in pursuit of a deeper understanding of sleep itself. [PERSON], [PERSON], and [PERSON] introduced the term Polysomnography in 1974. PSG is performed using an electronic device equipped to monitor multiple physiologic parameters during sleep by recording corresponding electrophysiological signals, for instance: from the brain via electroencephalogram (EEG), from the eyes via electrooculogram (EOG), from the skeletal muscles via electromyogram (EMG), and from the heart via electrocardiogram (ECG) [3]. To collect this data, recording devices are attached to the relevant locations of the body, typically including three EEG electrodes, one EMG electrode and two EOG electrodes. ECG is also a compulsory component of PSG. Additionally, the monitoring of respiratory functions may be desired in the diagnosis of respiratory disorders such as sleep apnea andrequire the addition of other tools applied in conjunction with the EEG electrodes, most often a pulse oximeter, oral thermometer, nasal cannula, thoracic and abdominal belt, and a throat microphone [4; 5]. Figure 1 represents the standard system used for measuring the EEG signal, termed as the 10-20 system, in which the minimum number of electrodes used is 21. This method regulates the physical placement and designations of electrodes on the scalp. The head is divided into proportions from important sites of the skull so that all areas of the brain are adequately covered. The label of 10-20 indicates that the actual distances between neighboring electrodes are either 10% or 20% of the distance from the nasion (front side of the head/anteriorly) to the inion (back side of the head/posteriorly) between the ears and nose where electrode points are chosen. Generally, electrodes marked with even numbers are placed on the right side of the head and those marked with odd numbers on the left side. The electrodes are also marked with letters to represent their locations relative to the anatomical divisions of the brain: F (frontal), C (central), T (temporal), P (parietal), O (occipital), and Fp (Frontal pole). A subscript z is used to mark the midline electrodes as zero. The electric signal in the brain is determined by measuring the difference of the electric activity between the two electrodes over a period of time. As it propagates, the signal gradually decays with distance from the source. Finally, the signal has a decreased value since only one of the parallel combinations of electrodes gives precise measurement [4; 6]. EEG waveforms have several kinds of rhythms. These rhythms are remarkably useful for classification annotation of sleep score as recorded by PSG. In a normal EEG, we differentiate these rhythms into five frequency bands. Table 1 lists the frequency and amplitude ranges of these bands [4; 7]  
Human sleep consists of cyclic stages, and the sleep stages are essential sections of activity during sleep. Three main stages of the sleep cycle are awake, non-REM (NREM) sleep, and rapid eye movement (REM) sleep. The NREM phase is also called dreamless sleep: breathing is slow and heart \begin{table}
\begin{tabular}{c c c} \hline \hline
**Bands** & **Frequencies (Hz)** & **Amplitude (\(\mu\)V)** \\ \hline Delta & 0.5–3.5 & 20–100 \\ Theta & 3.5–7.5 & 10 \\ Alpha & 7.5–12 & 2–100 \\ Beta & 12–30 & 5–10 \\ Gamma & \textgreater{}31 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Frequency and amplitude range of the EEG signal. Figure 1: Electrodes placement of electroencephalogram (EEG) measurement [4] (reproduced with permission by Elsevier (License Number 4781771458692)). rate and blood pressure are normal.