J. Biomedical Science and Engineering, 2011, 4, 207-213 JBiSE
doi:10.4236/jbise.2011.43029 Published Online March 2011 (http://www.SciRP.org/journal/jbise/).
Published Online March 2011 in SciRes. http://www.scirp.org/jour nal/JBiSE
Statistical analysis of epileptic activities based on histogram
and wavelet-spectral entropy
Ahmad Mirzaei, Ahmad Ayatollahi, Hamed Vavadi
School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran.
Email: ahmad.mirzaei.ce@gmail.com; ayatollahi@ iust.ac.ir; vavadi@elec.iust.ac.ir
Received 15 October 2010; revised 4 December 2010; accepted 7 December 2010.
Epilepsy is a chronic neurological disorder which is
identified by successive unexpected seizures. Elec-
troencephalogram (EEG) is the electrical signal of
brain which contains valuable information about its
normal or epileptic activity. In this work EEG and its
frequency sub-bands have been analysed to detect
epileptic seizures. A discrete wavelet transform (DWT)
has been applied to decompose the EEG into its
sub-bands. Applying histogram and Spectral entropy
approaches to the EEG sub-bands, normal and ab-
normal states of brain can be distinguished with
more than 99% pr obability.
Keywords: Electroencephalogram (EEG); EEG
Sub- Bands; Epileptic Seizures; Discrete Wavelet
Transform (DWT); Histogram; Spectral Entropy (SEN)
Physiological rhythms are important indicators of health.
Diseases which cause some irregularities in th ese rhythms
may lead to death. Epilepsy is a co mmon diso rder of th is
type. About 1% of the Americans are affected by epi-
lepsy [1].
Epilepsy is characterized by abnormal irregular firing
of neurons due to synchronous or excessive neuronal
activity in the brain. Due to high complexity of brain we
should apply several linear and non-linear signal proc-
essing methods to analyse Electroencephalogram (EEG)
signal truly. EEG signals extracted from the brain show
a non-stationary behaviour.
Duke and Pritchard studied about the chaos of brain.
They proved that, because of non-stationary behaviour
and complex dynamic of the brain, chaotic methods are
appropriate for EEG signal analysis [2]. Since the neu-
ronal activities in ictal, interictal, and healthy states sig-
nificantly differ from each other, chaotic methods such
as entropies can be applied to distinguish between these
three states [3].
It is helpful to use discrete wavelet transform (DWT)
because of its advantages such as time-frequency local-
ization, multi-rate filtering, and scale-space analysis [3].
EEG sub-bands have more accurate information about
neuronal activity compared to the original full spectrum
EEG. Also, DWT is a powerful transform to analyse
non-stationary sign als, because it has a good localizatio n
in both time and frequency domains [4,5]. Fast events
and changes in neuronal activities lik e spikes that are not
obvious in full spectrum EEG, can be recognized in
sub-bands. Thus to detect epileptic seizures accurately,
each sub -band should be analysed separately [3].
Recently, chaotic methods like correlation dimension,
largest Lyapunov exponent and entropies have been ap-
plied to EEG sub-bands acquired from preprocessing
analysis based on DWT [3]. Iasemidis and Sackellares
were the first researchers who studied the nonlinear be-
haviour of EEG and epilepsy [6]. They applied largest
lyapunov exponent as a chaotic parameter to show the
reduction of chaos in preictal phase [7,8]. Elger and
Lehnertz similarly concluded that complexity of neu-
ronal activities is reduced in preictal phase. They used
correlation dimension and moving-window dimension
analysis for patients with temporal lobe epilepsy [9,10].
Tayaranian et al. using three features; Detrended Fluc-
tuation Analysis (DFA), Bis-pectral Analysis (BIS), and
Standard Deviation (SD), for EEG analysis [11]. They
also apply a fuzzy classifier to separate the three groups.
Kumar et al. applied entropy method based on Shan-
non and spectral entropy and concluded that the Shannon
entropy value in ictal seizure activity is lo w compared to
healthy and interictal states. Also they reported that the
spectral entropy (SEN) value in normal and interictal
states is low compared to ictal state [12]. We previously
developed a method for distinguishing ictal state from
healthy one by calculating the SEN values for wavelet
coefficients of EEG and its sub-bands [13].
In this study the EEG signal has been decomposed
into five sub-bands by discrete wavelet transform (DWT).
Then histogram and Wavelet-spectral entropy have been
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
presented to analyse EEG sub-bands for epileptic sei-
zures detection. To validate the results statistical analysis
has been applied at the end of each process. The block
diagram of the procedure is depicted in Figure 1.
We applied our method to three different groups [14]:
1) Healthy subjects that contain state one and two,
corresponding eyes open and close d, respectively.
2) Interictal subjects (seizure-free intervals) that con-
tain two different sets: focal interictal activity and
non-focal interictal activity.
3) Ictal subjects (epileptic activity).
2.1. Description of the EEG Database
Our EEG data, acquired from university of Bonn, con-
tains three different cases: 1) healthy, 2) epileptic sub-
jects during seizure-free interval (interictal), 3) epileptic
subjects d u ring seizure interval (ictal) [14].
Each case has five datasets named: O, Z, F, N, and S.
Sets O and Z are obtained from healthy subjects under
condition of eyes open and closed; respectively by ex-
ternal surface electrodes. Sets F and N are attained from
interictal subjects.
Set F taken from epileptogenic zone of the brain
shows focal interictal activity; set N obtained from hip-
pocampal formation of the opposite hemisphere of the
brain indicates non-focal interictal activity, and set S is
got from an ictal subject.
Each set contains 100 single channel EEG segments
of 23.6 sec duration. Sampling frequency is 173.61 Hz,
so each segment contains N = 4096 samples [14]. All these
EEG segments are recorded with the same 128- channel
amplifier that converts by 1 2 A/D convertor with bit rate
of 12, and then were sampled on 173.61 Hz [14].
Since the sampling frequency of EEG records is
173.61 Hz, according to Nyquist sampling theorem,
maximum frequency of EEG applied should be in the
range 0-86.81 Hz. b ased on the physio logical research es,
frequencies above 60 Hz in EEG signal are considered
as noise and can be neglected [3]. Thus we have elimi-
nated these frequencies using a low-pass FIR filter.
2.2. Wavelet Decomposition
DWT is a proper transform to analyse signals in both
time and frequency domains. Using the multi-scale
Feature extraction Statistical
Feature extraction
Figure 1. Block diagram of proposed method.
form of DWT, signal can be decomposed into separate
frequency bands which each band represents a spe-
cific roughness. Wavelet transform uses a variable
window size over the length of the signal, which al-
lows the wavelet to be stretched or compressed de-
pending on the signal frequency [3].
In this study fifth-order Daubechies (DB5) DWT has
been applied to the band-limited EEG (0-60 Hz). After
the first level of decomposition, the band-limited EEG
has been decomposed into its high resolution frequency
band, D1 (30-60 Hz), and low resolution frequency band,
A1 (0-30 Hz), which should be decomposed in next level.
In the second level of decomposition, A1 has been de-
composed into its high, D2 (15-30), and low, A2 (0-15
Hz) resolution bands. This process has been repeated
four times. After full decomposition five sub-bands have
been attained: high frequency sub-bands (details) of lev-
els 1 to 4 (D1 (3 0-60 Hz) , D2 (15 -30 Hz), D3 (8-15 H z),
D4 (4-8 Hz)) as well as the low frequency sub-band (ap-
proximate) of the last level (A4 (0-4 Hz)). Figure 2 il-
lustrates this multi-level decomposition process sche-
These five frequency sub-bands are almost corre-
sponding to five physiological EEG bands, delta (0-4
Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-30), and
gamma (30-60 Hz).
2.3. Statistical Analysis of Histograms
Histogram is a visual feature for indicating the disper-
sion of EEG data. Each rectangle in the histograms
shows the population of samples falls into several bins
corresponding to different amplitudes in EEG sequence.
Plots of Figure 3 show outstanding differences in dis-
persion of data in histograms for epileptic patients in
conniption time from healthy and epileptic patients in
seizure-free interval. This led us to consider the histogram
Figure 2. Schematic of multi-level decomposition.
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
Figure 3. EEG histograms for five typical subjects.
as a criterion to assess epileptic seizures. To quantify the
discrepancies of the data distributions, mean and stan-
dard deviation (STD) have been calculated for each his-
togram. This has been repeated for all EEG sub-bands
and the results are reported in Table 1.
2.4. Statistical Analysis of Entropies
In this section we have applied the spectral entropy
method to differentiate between the mentioned cases.
After development of information theory scientists in-
troduced the concept of entropy [15]. Entropy expressed
first by Shannon in 1940s [15]. To calculate the spectral
entropy of a signal it is necessary to have the power
spectrum values. The square of the Fourier transform
is called power spectrum, which indicates the
distribution of signal energy in frequency domain [16]. It
should be noted that, the power spectrum is defined for
Ta bl e 1. Mean and standard deviations (in parenthesis) of his-
n = 100 Z
n = 100 F
n = 100 N
n = 100 S
n = 100
(0-60 Hz) –12.476
(61.012) –6.223
(40.641) –6.175
(65.503) –8.8518
(50.746) –4.8647
A4 (delta)
(0-4 Hz) –12.481
(29.63) –6.2259
(28.904) –6.1735
(56.911) –8.8561
(44.738) –4.8409
D4 (theta)
(4-8 Hz) 0.0044
(34.555) 0.0042
(18.188) –0.0001
(26.058) 0.0045
(19.136) –0.0309
D3 (alpha)
(8-15 Hz) 0.0014
(36.658) –0.0008
(18.813) –0.0011
(15.333) –0.0001
(11.667) 0.0016
D2 (beta)
(15-30 Hz) –0.0007
(13.055) –0.0005
(9.909) –0.0003
(6.4223) –0.0002
(5.4961) 0.0056
(30-60 Hz) 0.0001
(3.3764) –0.0001
(2.3939) 0
(1.643) 0
(1.5903) 0
stochastic and stationary processes, while the EEG sig-
nal is a stochastic and non-stationary sequence. Hence,
to assess the stationarity condition entire series have
been divided into 32 sub-segment (epoch). Each of these
sub-segments contains 128 samples with 0.74 second
duration. The value of spectral entropy for each epoch
has been calculated in the following steps:
Step 1: the power spectrum,
pf of the signal,
t has been calculated as:
 
dpf ftexjtt
where, equation
 
exp d
is continuous-time
Fourier transform.
Then, it has been normalized to its summation:
 
(0 1)
Qf Qf
Step 2: The Shannon function,
log 1
xx x has
been applied to the normalized power spectrum compo-
log 1
fQf Qf (3)
Step 3: Normalized entropy, SEN, has been calculated
Nf is the total number of frequency com-
ponents. Normalized entropy is a measure of regularity.
SEN value equal to one shows th e max i mum i rr eg ul ar it y,
and equal to zero shows the complete regularity. For
each 128 samples of power spectrum an entropy value
has been calculated. We have assigned the average value
of 32 entropies to each data-segment. This has been re-
peated for all 100 data-segments. Then, mean and STD
of these SEN values have been estimated for each band
limited EEG and its sub-bands. The results are collected
in Table 2.
Table 2. Mean and standard deviations (in parenthesis) of SEN
n = 100Z
n = 100 F
n = 100 N
n = 100S
n = 100
(0-60 Hz) 0.629
(0.073) 0.634
(0.085) 0.538
(0.093) 0.539
(0.091) 0.653
A4 (delta)
(0-4 Hz) 0.375
(0.09) 0.393
(0.097) 0.419
(0.096) 0.425
(0.097) 0.484
D4 (theta)
(4-8 Hz) 0.563
(0.074) 0.58
(0.063) 0.567
(0.071) 0.565
(0.067) 0.553
D3 (alpha)
(8-15 Hz) 0.641
(0.086) 0.69
(0.061) 0.684
(0.062) 0.685
(0.057) 0.667
D2 (beta)
(15-30 Hz)0.762
(0.055) 0.761
(0.055) 0.79
(0.053) 0.794
(0.05) 0.759
(30-60 Hz)0.786
(0.051) 0.81
(0.05) 0.821
(0.054) 0.822
(0.045) 0.871
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
3. Results
We have pointed to widespread shape of pure epileptic
histogram versus histograms of seizure-free and normal
intervals in section 2.3. Figure 4 depict this notion in
detail. Figures 4(a), (c), (e) show the EEG data r eco rded
from a typical healthy, interictal, and ictal subject, re-
spectively, and Figures 4(b), (d), (f ) display the corre-
sponding histograms. Comparison between these histo-
grams shows that, in ictal state EEG samples spread
(a) (b)
(c) (d)
(e) (f)
Figure 4. Band limited EEG data recorded from a typical healthy (a), interictal (c), and ictal (e) subject, respec-
tively, these corresponding histograms in (b), (d), and (f) respectively.
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
more than EEG samples obtained from healthy and in-
terictal cases. This uniformity in histogram of seizure
interval demonstrates the existence of high amplitude
samples as well as low amplitude ones. Table 1 shows
the means and standard deviations (STD) for all cases.
As we expected from histograms, the STD of the
band-limited EEG and its sub-bands in ictal state are
high compared to healthy and interictal states. This
shows the low frequency and high amplitude activity of
neurons in conniption time, while, in other cases the
brain has only a low amplitude activity. As we men-
tioned in section 2.4, SEN is an appropriate parameter to
separate normal and epileptic EEGs.
It is clear from Table 2 that for the band-limited EEG,
in ictal state the SEN value is high compared to normal
and interictal states. This result is similar to the result of
Kumar et al.’s work [12] and contravenes the physio-
logical aspects. Because according to physiological as-
pects the regularity should be increased on conniption
times. As mentioned above when regularity is increased
the entropy values tending to zero. Thus we conclude
that the SEN values in ictal state should be less com-
pared to interictal and healthy states. This result is not
satisfied in Kumar et al.’s work and in our study in
band-limited EEG. Thus we applied DWT to decompose
the band-limited EEG and evaluate its sub-bands but
Kumar et al. evaluate just band-limited EEG. This result
is repeated for delta (low frequencies) and gamma (high
frequencies) sub-bands. But, for middle sub-bands, theta,
alpha, and beta, SEN values of ictal state are low com-
pared to healthy and interictal states. These SEN values
of middle sub-bands satisfy the physiological aspect. It
can be seen that three middle sub-bands have the same
results as the results obtained from histogram analysis.
This implies that the regularity of EEG signal in its mid-
dle sub-bands increases in conniption time.
Comparison of three middle sub-bands shows that
unlike the beta sub-band in alpha and theta sub-bands
the disparity of the SEN values of the healthy and inter-
ictal subjects is negligible. Hence if the beta sub-band is
considered to be a representation of brain dynamics by
itself, the regularity becomes low in epileptic patients
during seizure-free interval.
Figure 5 shows the values of normalized SEN for the
typical band-limited EEGs and their beta sub-bands.
By means of T-Student distribution test1 we have
emphasized that in beta sub-band, healthy subjects can
be distinguished from epileptic patients during sei-
zure-free interval with more than 99% probability [17].
The probabilities of distinguishing between interictal
state and two other states in beta sub-band are shown in
Table 3.
In fact in this study we focus on comparison between
interictal state and healthy and ictal states, because it is
clear that for prevention treatments we should evaluate
the interictal activities to help prevent the seizure. Table
4 shows the comparison of our result and kumar et al.
result based on Spectral entropy. Their results are for
band limited EEG that do not satisfy physiological as-
pect totally but our results are for beta sub-band that
satisfy physiological aspect and achieve better results.
As we see from Table 4 that we compare the focal and
non-focal interictal with ictal, separately.
4. Conclusion
Two methodologies based on statistics and chaos theory
in time-frequency domain have been presented for anal-
ysis of EEGs and its delta, theta, alpha, beta, and gamma
sub-bands for detection of epilepsy. Since the EEG is an
overall representation of brain dynamics, the observed
changes in the band-limited EEG are actually the result
of the total activity of neurons which performs a sub-
stantial role in forming the shape of the EEG signal. One
method of studying these underlying activities are to
study the component physiological sub-bands of the
EEG which can be assumed to represent the neurological
activities at a finer level. It has been shown that the sta-
tistical analysis of histograms of EEGs and their sub-
bands can reveal the differences between frequencies
dependent amplitudes of EEG signal in ictal state from
healthy and interictal states. It has been observed that the
spectral entropy of the band-limited EEG can distinguish
between the three groups of subjects. The decomposition
of the original EEG into its five constituent sub-bands
alters the results obtained from original signal. However,
when the statistical analysis is performed on the EEG
sub-bands, it can be seen that the SEN used within cer-
tain physiological sub-bands may also be employed to
distinguish between all three groups. Therefore, it has
been emphasized that changes in the dynamics are not
spread out equally across the spectrum of the EEG, but
instead, are limited to certain frequency bands.
Table 3. Probability of differentiation between a typical inter-
ictal case and two other cases in healthy and ictal state.
F – OF – ZF – S N – O N – Z N – S
beta99.9%99.9%99.93% 99.94% 99.94%99.95%
Table 4. Comparison of our work and Kumar et al.
Comparison between F, N, and S states
Kumar et al. 94.6%
Comparison between F
and S Comparison between N
and S
Our work
99.93% 99.95%
1For more information refer to Appe n di x .
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
(a) (b)
(c) (d)
(e) (f)
Figure 5. Comparison of normalized SEN values of typical EEGs and their beta sub-bands between healthy and interictal (a), (b),
healthy and ictal (c), (d), and ictal and interictal (e), (f) states.
A. Mirzaei et al. / J. Biomedical Science and Engineering 4 (2011) 207-213
Copyright © 2011 SciRes. JBiSE
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1. Two- Sample t Test
T-Student is applied to two independent samples to esti-
mate the probability (p-value) of distinguishing between
two populations means.
t is the T-student test and 2
and 2
are samples
variances. 1
and 2
are means of samples. 1
n and
n are sample intervals that are equal 12
100nn . To
obtain the p-value, T-Student degrees of freedom, d
should be calculated as:
 
 
 
We can read p-value from the T-Student table (A.1)
that is arranged according to t and d
calculated by above equations.