Time-Frequency Analysis of EEG Data to Diagnose Epilepsy by Using Wavelet Power Spectrum & Global Wavelet Spectrum
Abstract: The electroencephalography (EEG) is a way to study the individual’s electrical activity of the brain. It is non-invasive technique to analyze brain signals which help to identify that either signals are showing normal or abnormal activity of the brain i.e. epilepsy or other neurological disease. The signals of EEG are non-stationary means the frequency of signals changes over time. To study these non-stationary signals, wavelet transform is used to classify EEG segment for epileptic patient. In the proposed work, wavelet power spectrum (WPS) and global wavelet spectrum (GWS) are applied on three EEG datasets to compare the results of epileptic and healthy person.

Introduction
Brain has a very tremendous importance in individual’s life. It consists of millions of nerve cells that are interconnected with each other. All our actions, thoughts and activities are carried out due to electrical impulses that travel along neurons from the body to brain. These electrical signals are divided into five different waveform based on their frequency range which corresponds to different activities carried out by the subject. Generally, in normal persons, the frequency range of brain waves are as follows: Delta (0-4 Hz), Theta (4-8 Hz), Alpha (8-12 Hz), Beta (13-30 Hz) and Gamma (30-60 Hz) while the abnormality in fluctuations of electrical signals show brain disorders such as epilepsy, autism spectral disorder (ASD) and other neurological diseases.
The diagnosis of abnormality is an important issue. For this, various techniques have been introduced to measure brain activity to diagnose epilepsy or other neuro diseases such as functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), positron emission tomography (PET), electroencephalography (EEG) etc. 1. Among all these methods EEG is one of the most widely used method to measure brain activity.

EEG signals possess meaningful information about the function of the brain by capturing electrical signals of the brain 2. As EEG signals are non-stationary in nature and long term EEG measurements has a lot of data values which is difficult to review manually 9. Therefore time varying computation is needed to extract the useful information from EEG signals. For this purpose there are variety of mathematical methods to study the time series that contain non stationary power at many different frequencies. The most appropriate method to analyze localized variations of power within a time series is wavelet transform.

Wavelet transform provides information on both the amplitude of any periodic signal within the series and time at which the amplitude of signal varies 3. Wavelet transform are either discrete or continuous. In this paper we used continuous wavelet transform to differentiate healthy person and epileptic patient with the help of wavelet power spectrum and global wavelet spectrum.

Materials and Proposed Methodology
1) Dataset obtained
The data used in this paper is obtained from Epilepsy center in Bonn, Germany collected by Dr. Ralph Andrzejak which is publically available (http://epilptologiebonn.de/) 7. The acquired data consists of five EEG datasets (A-E). Each containing 100 single channels EEG signal of 23.6 sec duration at a sampling rate of 173.61 Hz. We used three datasets in this paper which are set A, B and E. Set A contains Z001 from class Z, set B contains O001 from class O and set E contains S001 from class S . Set A represents healthy subject with eyes open, B represents eyes closed and E represents seizure activity. These three EEG signals are shown in fig 1.

2) Wavelet transform
Wavelet analysis has a broad aspect to analyze signals in time-domain 1. Wavelet transform is a mathematical tool for time-scale analysis, signal decomposition and signal compression 10. There are two types of wavelet transform which are: i) Discrete wavelet transform, ii) Continuous wavelet transform.

In this paper, we used CWT for three EEG datasets with Morlet wavelet function by the reference of Torrence & Compo, which is defined as 8:
?0?=?-14ei?0?e-?22(1)
Where ?0 and ? represent frequency and time which has no dimension respectively.

And the CWT of discrete sequence of EEG signal ‘Sign’ is defined as a convolution of the data sequence with a scaled and translated version of the mother wavelet 11. Mathematically 8:
Ws=?tsn=0N-1Sign?*n-m?ts(2)
m=0,1,…, N-1.

Where operator * expresses conjugate complex value, N is the number of points in the time series, ?t is sampling interval and s & m are dilation & translation parameter used to change the scale & slide in time respectively with wavelet function ?.

Figure 1: EEG signals a) Z001, b) O001, c) S001
a) Wavelet power spectrum
Wavelet power spectrum allows to determine the energy distribution within the data array where large power in WPS shows that which features of signal are important to compute and which are not 4. Mathematically it is the absolute value squared of wavelet transform coefficients (Eq 2) denoted as:
Ws2Wavelet power spectrum of selected three EEG datasets are shown in Figure 2.

Figure 2: Wavelet power spectrum of signals Z001, O001 and S001 are shown in left panel of a, b and c respectively with cone of influence indicated by black curve. Below this curve, values are not statistically significant. Global wavelet spectrum of signals Z001, O001 and S001 are showing in right panel of a, b and c respectively. Wavelet power decreases according to the color order as: red, orange, yellow, blue and white
b) Global wavelet spectrum
Global wavelet spectrum provides a fair and consistent estimation of the true power spectrum of the time series. It is also helpful in comparing the region’s temporal variability to the other regions which does not display long term changes 5. The GWS (time averaged wavelet spectrum) is defined as 6:
W2 s=1Nn=0NWs2(3)
Results and Discussions
Figure 2 is plotted by using software tool available at: http://paos.colorado.edu/research/wavelets/ in which the wavelet power spectrum and global wavelet spectrum of three EEG signals are compared. It is clear from Figure 2 that the difference in the magnitude of the EEG signal S001 component in the frequency period around 4-8 Hz (theta wave) and 8-16 Hz (alpha wave) is significant different from the same component of the EEG signals Z001 and O001. To quantify the difference among all three signals, the statistical feature (variance) of these signals is calculated in Table 1 which clearly show the difference in epileptic patient, healthy person with eyes open and eyes closed.

Table 1: Variance of EEG signals S001, Z001 and O001
______________________________________________________________________________
Brain wavesS001Z001O001
Alpha4.1656e+003157.6744328.8349
Theta1.1900e+003151.0412174.5409
Conclusion
In this study, healthy and epileptic persons are classified using EEG data based on wavelet analysis. Wavelet analysis is applied to characterize EEG signal frequency component along with time localization on three EEG datasets. WPS and GWS clearly indicated the difference in activities of examined groups.

References
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6 “Diagnosis of epilepsy from EEG signals using global wavelet power spectrum”, Samir Avdakovic, Ibrahim Omerhodzic, Almir Badnjevic, and Dusanka Boskovic7 Andrzejak RG, Lehnertz K, Rieke C, Mormann F, David P, Elger CE. Indications of nonlinear deterministic and finite dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64(6 Pt 1):061907. Online available at: http://epileptologie-bonn.de/cms/front_ content.php?idcat=193;lang=3;changelang=3.
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9 ch 1 introduction
10 wavelet transform use for feature extraction and EEG signal segments classification
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