Engineering, 2013, 5, 15-19
doi:10.4236/eng.2013.55B004 Published Online May 2013 (
Selection of a Suitable Wavelet for Cognitive
Memory Using Electroencephalograph Signal
S. Z. Mohd Tumari, R. Sudirman, A. H. Ahmad
INFOCOMM Research Alliances, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru, Malaysia
Received 2013
The aim of this study is to recognize the best and suitable wavelet family for analyzing cognitive memory using Elec-
troencephalograph (EEG) signal. The participant was given some visual stimuli during the study phase, which were a
sequence of pictures that had to be remembered to acquire the EEG signal. The Neurofax EEG 9200 w as used to record
the acquisition of cognitiv e me mory at channel Fz. Th e raw EEG signals were analyzed using W avelet Transform. A lot
of mother wavelets can be used for analyzing the signal, but do not lose any information on the wavelet, some predic-
tions must be made beforehand. The criteria of the EEG signal were narrowed down to the Daubechies, Symlets and
Coiflets, and it is the final selection depending on their Mean Square Error (MSE). The best solution would have the
least difference between the origin al and constructed signal. Results in dicated that the Daubechies wavelet at a lev el of
decomposition of 4 (db4) was the most suitable wavelet for pre-processing the raw EEG signal of cognitive memory. To
conclude, choosing the suitable wavelet family is more important than relying on the MSE value alone to successfully
perform a wavelet transformation.
Keywords: EEG; Wavelet Families; MSE; Visual Stimuli; Daubechies
1. Introduction
Working memory and short term memory storage are
always related to each other, but the former can actually
improves the exploration of other complex cognitive
tasks more than the latter. These relationships emphasize
more on the common processing demands of working
memory and complex cognitive tasks rather than storage
issues. Recent researches [1] in working memory include
making a distinction between what have been developed
to be recognized as simple or complex spans. Complex
span tasks are to-be-remembered things interleaved with
several outlines of disturbing task, for example, solving
mathematics question and reading sentences [2]. Simple
span tasks, on the other hand, are related to the combina-
tion of both unloading primary memory and secondary
memory, such as words and letters [3]. In this study,
more attention is given to complex span activities.
2. Wavelet Algorithm
Wavelet algorithm provides a way of representing a time
frequency in a certain sized variable window. It also
transforms the Electroencephalograph (EEG) characteris-
tics to allow further extraction and classification because
these signals are non-stationary [4]. The advantages of
using wavelet transformation are different from Fourier
transformation because this type of transformation can
capture the transient features in a given signal and pro-
vide the corresponding time frequency information. In
this study, the Discrete Wavelet Transform (DWT) was
chosen to decompose the signal through the means of
low-pass and high-pass filtering into two components,
which are the low an d high frequ ency proportion, resp ec-
tively, of the signal [5]. In real life problem, DWT is
more suitable in area of biomedical applications. DWT
determination examines the signal at different frequency
bands with different resolutions by decomposing the
signal into Approximation coefficients (cA) and detailed
information (cD). In short, this algorithm gives precise
analysis of frequency domain at low frequency and time
domain at high frequency [6].
2.1. Types of Wavelet Families
The different types of wavelet families in Matlab are as
shown in Table 1. An Electroencephalograph signal can
be categorized into orthogonal, symmetry, compact sup-
port, and non-stationary signals, but these signals can be
further classified into smaller scopes (wavelet families)
according to their characteristics and properties. The
EEG signal in this study is a form of orthogonal signal,
and is filtered using the finite impulse response (FIR)
filter. Not all wavelet families fulfill the properties of
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such signal. The wavelet chosen has to be as close as
possible to the analyzed signal to give a better recon-
struction with fewer decomposition levels.
An orthogonal signal is important because [7]:
1) It conserves the energy of the signal throughout the
wavelet transform so that no information will be lost.
2) It allows wavelet transformation that can extract
high and low frequency details.
The finite impulse response (FIR) filter gives compact
support that is very useful for transien t signal analysis (non-
stationary signal) [7] because its wavelets are smoother
and can enh ance the illustration of transients in th e signal.
Besides that, such compact support also allows the
wavelet transform to efficiently characterize the signals
that contain the features’ information.
Wavelet families such as Haar, Daubechies, Symlets,
and Coiflets have sufficient properties to analyze signal
acquisition. The Haar wavelet, in particular, is comprised
of a Daubechies order of 1 (db1). In this study, since the
reconstruction criterion was evaluated using a coefficient
number that had to be more than two, the Haar wavelet
was excluded from the list. The Morlet and Mexican Hat
wavelet families were not included as well because they
could not fully reveal the characteristics essential for
biomedical areas [8,9]. To find the appropriate wavelet
family for the EEG signal, several calculations had to be
performed and this will be discussed further.
2.2. Choice of Level Decomposition
To perform the required decomposition, the output sig-
nals having half the frequency’s bandwidth from the
original signal have to be down-sampled by 2 using the
Nyquist rule [10]. According to th is rule, an original sig-
nal has a highest frequency of ω, this requires a sampling
frequency of 2ω before it can be down-sampled to ω/2
Table 1. Types of wavelet families [6].
No Wavelet Families Descriptions
1 Morlet (mor1) This wavelet has no scaling function but is
2 Mexican Hat
This wavelet has no scaling function and is
derived from a function that is proportional to
the second derivative function of Gaussian.
3 Meyer (meyr) Scaling function is defined in the frequency
4 Haar (haar) Discontinuous and resembles a step function.
Haar represent as Daubechies db1.
5 Daubechies (dbN) One of the brightest stars in the world of
wavelet research.
6 Symlets (symN) This wavelet is modification to the db family.
7 Coiflets (coifN) Built by I. Daubechies that has 2N moments.
8 Splines biothorgonal
wavelets (biorNr.Nd) This wavelet needed two wavelets for signal
and image reconstruction.
[11]. Without losing any information, the down-sampling
of a time domain signal can be divided into two - low and
high filtering. Down-sampling occurs when the original
signal, x(n), passes through a half band high-pass filter,
g(n), (detail coefficient) and then a low-pass filter, h(n)
(approximation coefficient) [12]. A one level of decom-
position can be mathematically expressed as in Equation (1),
(2) and (3) [13].
where yhigh[k] an d ylow[k] are the outputs of the high-pass
and low-pass filters after being sub-sampled by 2.
In accordance to the theory presented above, the sev-
enth level wavelet decomposition was selected since the
frequency sampling used in this study was 500 kHz. In
this representation, the coefficients A1, D1, A2, D2, A3,
D3, A4, D4, A5, D5, A6, D6, A7, and D7 were the fre-
quency content from the original signal within the bands.
The extracted wavelet coefficients provided a compact
representation of different frequency ranges, as shown in
Figure 1 and Table 2. Figure 1 shows that , origi nal sig-
nal content the length of frequency is 500 and from 500
lengths it will down sampling by 2. Low frequency con-
tents length from 0 to 250 as name as approximation co-
efficient (A1) and high frequency (250 to 500) as a de-
tailed coefficient (D1). Then, A1 (low frequency) will
continue down sampling by 2 which are A2 (0 to 63) and
D2 (63 to 250). The pro cesses of down sampling resolve
interchange until the original signals find all the fre-
quency ranges. Table 2 shows that the frequency ranges
perform after 7 levels of decompositions. Wavelet trans-
form coefficients between two levels of details were de-
creased by 1 [14]. In particular, D4, D5, D6, and D7 had
62, 30, 15, and 7 coefficients respectively.
2.3. Choice of Wavelet Families
Our choice of wavelet families depended on the best re-
construction in term of mean square error (MSE), which
is the difference between the original signal, x(n), and
compressed signal,
(n). To analyze the Electroencepha-
lograph signal, the MSE must b e low. The reconstruction
criteria are calculated using Equation (4) [15].
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Table 2. Decomposition of EEG Signal into Different Fre-
quency Bands (Fs = 500 Hz).
Frequency Range (Hz)Decomposition Level Frequency Band
250 - 500 D1 Noise
125 - 250 D2 Noise
63 -125 D3 Noise
31 - 63 D4 Gamma
16 - 31 D5 Beta
8 - 16 D6 Alph a
4 - 8 D7 Theta
0 - 4 A7 Delta
Figure 2 shows the comparison between wavelets in
terms of mean square error. The results showed that db4
had a low MSE (0.32264 µV). Even though the MSE for
coif5 (0.31606 µV) was lower, the difference between
compressed and original signals were higher, so it was
postulated that some information were missing. In a nut-
shell, our results showed that the signals were within the
Daubechies wavelet family, which means that the signals
are regular orthogonal signals that have been compactly
supported to give the smallest size.
Figure 1. Seventh Level Wavelet Decomposition with detail
and approximation coefficients of signal.
Figure 2. Description of MSE between Original Signal and Reconstructed Signal among Wavelet Families.
3. Methodology
3.1. Participant
Our preliminary study involved a child who was aca-
demically the best in the class. This child loves to read,
has no record of brain injury, is active in school, and is a
prefect. The child was given some visual stimuli to in-
vestigate the responses of the brain activity while re-
membering the sequence of the pictures. The child was
asked to relax for two minutes before the assessment
3.2. Assessment Tasks: Study Phase
At this stage, the child was asked to look through a few
pictures shown on a computer’s screen. Figure 3 shows
four sample pictures that were presented to the child.
Every picture was displayed for 5 seconds and the whole
sequence was repeated twice. After that, the examiner
asked the child a few questions about the pictures and the
child’s responses in this recognition test was recorded
using the EEG machine.
4. Simulation
The raw EEG signals obtained from this study, unsur-
prisingly, also contained artifacts or noises. These artifacts
were then filtered off b efore furth er analysis. An important
point to note is that EEG signals are frequently quantified
based on their frequency domain characteristics. There-
fore, in order to extract useful information from the EEG
signals (mean, standard deviation and maximum value),
Discrete Wavelet Transform had to be applied. This was
to simplify and extract the information from different
frequency bands (alpha, beta, delta, theta and gamma) by
decomposing the signals into approximate coefficients
and detailed information. The multi-resolution analysis
was then performed with the Daubechies wavelet set at 4
(Db4) and the level of decomposition set at seven (cD7).
Figure 4 shows the information from sub-band 4 to 7
(gamma, beta, alpha, theta, delta) calculated for further
analysis. The information was extracted during the as-
sessment of the study phase. Then, based on the sub-band
signal, the highest power spectrum distribution for each
frequency determinati on was det e r mined.
As shown in Figure 5 and summarized in Ta bl e 3 , the
Theta band (D7) had improved the child’s visual re-
sponse and cognitive memory development. From the
graph of channel Fz, the power spectrum density (PSD)
at the theta band was the highest (127 V). This showed
that the child, theoretically, was in a deep relaxation
mood and was focusing on the task gi v en.
5. Conclusion
Choosing the best wavelet is more crucial for a successful
wavelet transform to avoid highly complex and lengthy
level decomposition. This is even more important than
relying on the value of MSE alone. In this study, our re-
sults have shown that the db4 wavelet family is the best
Figure 3. Study phase.
Figure 4. Detail Coefficients of Sub-band 4 to 7 of EEG
Signal at Channel Fz.
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Figure 5. (a) Beta (b) Alpha (c) Theta (d) Delta: Frequency
Domain of EEG Signal for First Subject at Channel Fz.
Table 3. Description on parameter extraction of eeg signal
for study phase: first subjec t.
(D5) Alpha
(D6) Theta
(D7) Delta
Mean 0.0289 0.3619 1.091 - 2.559
Standard Deviation 368.7 509.5 747.4 1183
Max Value 1703 2372 2054 2888
Median 146.3 320.5 438.3 856.9
PSD (µV) 5.82 0.101 0.013 0.011
Frequency (Hz) 9.77 5.86 1.95 0.98
for extracting the EEG signals into different frequency
6. Acknowledgements
Our appreciation also goes to the Malaysia Ministry of
Education, Johor Education Department, Zamalah Schol-
arship and Universiti Teknologi Malaysia for permission,
facilities and funding this project under QJ130000.
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