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World Academy of Science, Engineering and Technology 3 2007EEG Waves Classifier using Wavelet Transformand Fourier TransformMaan M. ShakerWillians filtering are used for the extraction of the featuresfrom each EEG channel, and NN is used as task classifier(these tasks include: open eye, mouse forward, mousebackward and standing). Khidhir A.S. M. (2000) proposed aprocedure to study the human state or movement (these statesinclude: open eye, mouse forward, mouse backward, andstanding) from EEG signal only [6]. The autocorrelation,wavelets, and Principal Component Analysis (PCA) were thetypes of the processing used. The Neural Network (NN) isused to recognize the state. The autocorrelation signal is usedinstead of the signal itself to decrease the complexity of theNN. PCA is used to reduce the dimensionality of the EEGsignal. Finally, wavelet analysis is used as a classifier prior tothe NN.The aim of this work is to calculate the EEG waves (delta,theta, alpha, and beta) using Discrete Wavelet Transforms(DWT) followed by discrete Fast Fourier Transform (FFT).Abstract—The electroencephalograph (EEG) signal is one of themost widely signal used in the bioinformatics field due to its richinformation about human tasks. In this work EEG wavesclassification is achieved using the Discrete Wavelet TransformDWT with Fast Fourier Transform (FFT) by adopting the normalizedEEG data. The DWT is used as a classifier of the EEG wave’sfrequencies, while FFT is implemented to visualize the EEG waves inmulti-resolution of DWT. Several real EEG data sets (real EEG datafor both normal and abnormal persons) have been tested and theresults improve the validity of the proposed technique.Keywords—Bioinformatics, DWT, EEG waves, FFT.I. plex irregular signals that may provide informationabout underlying neural activities in the brain [1].Electroencephalograms are recordings of the tiny electricalpotentials (generally less than 300µV) produced by the brain[2-3].The brain waves recorded from the scalp have smallamplitude of approximately 100µV. The frequencies of thesebrain waves range from 0.5 to 100 Hz, and their characteristicsare highly dependent on the degree of activity of the cerebralcortex [4]. Generally, in normal persons, the brain waves maybe classified as belonging to one of four wave groups. Thespectra of these waves are called [3]:1. The Delta waves which include all the waves in the EEGbelow 3.5 Hz. They occur in deep sleep, in childhood, and inserious organic brain disease.2. The Theta waves have frequencies between 4 and 7 Hz.These occur mainly during the childhood, but they also occurduring emotional stress in some adults.3. The Alpha waves are rhythmic waves occurring at afrequency range between 8 and 13 Hz, which are found in allnormal persons when they are awake in a quiet, resting state ofcerebration.4. The Beta waves are very low amplitude, and highfrequency range between 13 and 30 Hz. They are affected bymental activity.Many researchers tried to investigate these EEG wavesactivities recently. Suleiman A.B. R. (2001) proposed a newapproach for describing and classifying the EEG brain naturaloscillations (delta, theta, alpha, and beta) frequencies usingWigner-Ville analysis with Choi-Willians filtering and NeuralNetwork (NN) [5]. The Wigner-Ville analysis and Choi-EII. THEORETICAL CONCEPTS: DISCRETE WAVELETTRANSFORMS (DWT)The DWT means choosing subsets of the scales ( a ) andpositions ( b ) of the wavelet mother ψ (t ) .a aψ (a ,b ) (t ) 2 2 ψ (2 2 (t b)) .(1)Choosing scales and positions are based on powers of two,which are called dyadic scales and positions { a j 2; b j ,k 2 j jk } ( j and k integers). Equation (1) shows thatit is possible to built a wavelet for any function by dilating afunction ψ (t ) with a coefficient 2 , and translating theresulting function on a grid whose interval is proportionalj jto 2 [7].Contracted (compressed) versions of the wavelet functionmatch the high-frequency components, while dilated(stretched) versions match the low-frequency components.Then, by correlating the original signal with wavelet functionsof different sizes, the details of the signal can be obtained atseveral scales. These correlations with the different waveletfunctions can be arranged in a hierarchical scheme utiondecomposition algorithm separates the signal into “details” atdifferent scales and a coarser representation of the signalnamed “approximation” [8-10].The algorithm of the DWT decomposition andreconstruction can be summarized by following procedure:Dr. Maan M. Shaker is assistance professor in OptoelectronicsEngineering, Technical College of Mosul, Mosul, Iraq (e-mail:maanms 56@yahoo.com).723

World Academy of Science, Engineering and Technology 3 2007 Given a signal “s” of length n. Starting from s, the first stepproduces two sets of coefficients: approximation coefficientscA1, and detail coefficients cD1. These vectors are obtainedby convolving s with the low-pass filter Lo D forapproximation, and with the high-pass filter Hi D for detail,followed by dyadic decimation. This is shown in Fig. (1.a).The length of each filter is equal to 2N. If n length (s), thesignals F and G are of length n 2N - 1, and then thecoefficients cA1 and cD1 are of lengthfloor (n 1) N2Fig. 2 The tree of the multi-decomposition (multi-level) of thesignal s(2)Floor means that the length of the coefficients rolled to thenearest integer. The next step splits the approximation coefficients cA1into two parts using the same scheme, replacing s by cA1 andproducing cA2 and cD2 as shown in Fig. (1.b), and so on. So,the wavelet decomposition of the signal s analyzed at level ihas the following structure: [cAi, cDi. cD1]. The structure in Fig. 2 contains i 3, as shown in theterminal of the tree. Conversely, starting from cAi and cDi, the inverse discretewavelet transform (IDWT) reconstructs cAi-1, inverting thedecomposition step by inserting zeros and convolving theresults with the reconstruction filters, as shown in Fig. 3 [8],[10].III. EEG WAVES CLASSIFICATIONThe discrete wavelet transform (DWT) has main advantagesover many conventional methods in the separation of waves. Itprovides an optimal resolution in both the time and thefrequency domains (i.e., dividing the signals into variousmulti-level frequencies), and it eliminates the requirement ofsignal stationary [9].Fig. 3 The algorithm of the IDWTThe proposed approach is summarized in the followingsteps:A. Normalizing the DataBrian waves occur during the activity of brain cells andhave frequency range (3-30) Hz [2]. The signal should benormalized prior to any analysis on the EEG waves to rejectundesired signals. The normalization is performed by bandpass filtering the signal (3–30) Hz (four poles Elliptic filter isused), and then signal amplitude is carefully adjusted.B. Data Decomposition using DWTDWT chooses only a subset of scales and positions. DWTworks as filters where the signals are divided into two bands ateach a specified level called approximations and detailssignals. The approximations (A) are the high-scale, lowfrequency components of the signal. The details (D) are thelow-scale, high-frequency components. The samples of thesignal are dividing by 2 and this is called sub-sampling, asshown in Fig. 4. The data obtained after normalization stageserves as the input data to the DWT decompositions, which isalso known as Sub-band Coding, and could be repeated forfurther decomposition. At every level, the sub-sampling willFig. 1 The algorithm of the DWT, (a) one decomposition of thesignal s, (b) decomposition at each level724

World Academy of Science, Engineering and Technology 3 2007result in half the number of samples. The procedure of thesub-band coding of the EEG data can be visualized [11], asshown in Fig. 5. In this work, a four-level multi-resolutiondecomposition using Daubechies4 wavelets is implemented.Each level could characterize the frequencies of the EEG databand.Fig. 4 The filtering process of the DWTC. Fast Fourier Transform (FFT) of each level in DWTlevels:Fourier analysis is extremely useful for data analysis, as itbreaks down a signal into constituent sinusoids of differentfrequencies. For sampled vector data, Fourier analysis isperformed using the discrete Fourier transform (DFT). Thefast Fourier transform (FFT) is an efficient algorithm forcomputing the DFT of a sequence; it is not a separatetransform. It is particularly used in area such as signalprocessing, where its uses range from filtering and frequencyanalysis to power spectrum estimation [9], [12]. Computationusing FFT of each level gives an indication to the frequenciesthat the bands contained in. Fig. 6 summarizes the flow chartof the EEG waves classification software.Fig. 6 Flow chart of EEG waves classification procedure.IV. PRACTICAL RESULTSThe EEG real data were recorded for both normal personsand epilepsy persons. The data were recorded as occipitalregion “O1” with earlobe “A1” as reference electrode .Thedata were transferred to the computer using NI-PCI-6023EDAQ, with sampling rate of 12 kHz. The length of each datarecorded is 10 sec (i.e. 120000 samples)[13]. Then, theamplitude of EEG data is normalized at ( 1) to be suitable forthe analysis.EEG waves classification contains two main processes: (a)EEG filtering, and (b) decomposition of the filtered signals.A. EEG Data FilteringThe digital filter used in the EEG waves classification is 4thorder pass band Elliptic filter, and the setting of the band passfrequencies is from (3-to-30) Hz. The filtered signals haveonly EEG waves (delta, theta, alpha, and beta) so this meansthat undesired frequencies (such as spikes) have been rejected.Fig. 7 shows the EEG data after filtering using the describeddigital filter. The main feature extracting from this Fig. is thatthe signals contain low frequencies. Figs. (7.a.1) and (7.b.1)represent the raw data before filtering for both the real data ofnormal person, and real data of abnormal person, respectively.Figs. (7.a.2) and (7.b.2) represent the filtered data for the sametwo persons above.Fig. 5 Sub-band coding algorithm of the DWT725

World Academy of Science, Engineering and Technology 3 20071.51.AmplitudeAmplitudeFrequency content of 4.(a.1)1.5111.522.53Time 0.5-0.5-1-10.511.522.5Time (sec)(b.1)33.544.55-1.50.0200.511.522.5Time (sec)33.544.55(b.2)0.01Fig. 7 The data before and after filtering for normalperson and abnormal person, where the left columnrepresents the raw data and right column represents thefiltered data0050100150frequency (Hz)(a)-64x 10Frequency content of D13.532µV /Hz2.521.510.50050100150frequency (Hz)(b)-54x 10Frequency content of D23.532µV /Hz2.521.510.50050100150frequency (Hz)(c)-4x 10Frequency content of D31.81.61.42µV /Hz1.210.80.60.4Fig. 8 Multi-level decomposition of real data of normal person0.20050100150frequency (Hz)(d)-3x 10Frequency content of D41.41.210.82µV /HzAmplitude0.51.50.5-1.5 0052-0µV /Hz-1.50.60.40.20050100150frequency (Hz)(e)Fig. 10 FFT of each DWT level of real data of normal person726