50120130406044

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING &
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME

TECHNOLOGY (IJCET)

ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 4, Issue 6, November - December (2013), pp. 403-413
© IAEME: www.iaeme.com/ijcet.asp
Journal Impact Factor (2013): 6.1302 (Calculated by GISI)
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IJCET
©IAEME

PROCESSING OF EVOKED POTENTIALS BY USING WAVELET
TRANSFORMS
G. Hemalatha1

Prof. B. Anuradha2

Prof. V. Adinarayana Reddy3

KSRMCE, Cuddapah

SVUCE, Tirupati

GPREC, Kurnool

ABSTRACT
We present a regular denoising method based on the wavelet exchange to obtain single trial
evoked potentials. The method is based on the inter- and intra-scale variability of the wavelet
coefficients and their deviations from baseline values. The concert of the method is tested with
simulated event related potentials (ERPs) and with real visual and auditory ERPs. For the simulated
data the presented method gives a significant improvement in the observation of single trial ERPs as
well as in the estimation of their amplitudes and latencies, in comparison with a standard denoising
technique (Donoho's thresholding) and in comparison with NZT algorithm. For the real data, the
proposed method (EMD denoising method) largely filters the spontaneous EEG activity, thus helping
the identification of single trial visual and auditory ERPs. The proposed method provides a
uncomplicated, automatic and fast tool that allows the study of single trial responses and their
correlations with behavior.
1. INTRODUCTION
Event related potentials (ERPs) are voltage fluctuations within the Electroencephalogram
(EEG) due to external stimulation or internal processes. They are routinely used for clinical
diagnosis, as they allow the identification of dysfunctions along the visual, auditory and
somatosensory pathways (10). ERPs are also widely used in neuroscience research, given that the
amplitude, latency and localization of different peaks or oscillatory patterns have been correlated to a
large variety of sensory and cognitive functions (17) gold standard in neuroscience, ERPs, and EEGs
in general, give only an indirect and noisy measure of the neuronal activity. The large advantage of
ERPs, however, is that, unlike single-cell recordings which are rarely performed in humans (12,20),
their recording involves a non-invasive procedure with a relatively simple setup, and therefore, they
continue to be one of the preferred tools for studying sensory and cognitive processes in human
subjects.
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One of the main problems in the analysis of ERP data is that the single-trial responses have a
small amplitude compared to the ongoing EEG in which they are embedded. By far the most popular
technique to enhance the observation of ERPs is by averaging several repetitions of the stimulus
(11). However, the drawback of ensemble averaging is that critical information about trial-by-trial
changes of the evoked responses is lost. In particular, the conventional approach in the design of an
ERP paradigm is to try to avoid these single-trial fluctuations in order to get better-defined average
responses. But there are many interesting questions that are in fact related to systematic or
unsystematic trial-by-trial variations, such as those related to the study of learning processes (19).
Thus the need to develop algorithms to filter the background EEG activity in order to observe the
single trial evoked responses. For this, the use of Wiener filtering was suggested. Wiener filtering
minimizes the mean square estimation error of average evoked potentials and could in principle be
used to denoise single trials. However, it is a time-invariant method—i.e. it assumes stationary of the
signal—and it does not give optimal results when dealing with time-varying transient signals such as
ERPs (6,9). For the same reason, other standard digital filters are not suitable for the analysis of
single-trial ERPs, given that ERPs are a series of waves appearing at different times and with
different frequency compositions. To deal with the non-stationary issue, De Weerd and co-workers
proposed a time-varying Wiener filter, which, however, could not provide a good reconstruction of
the signal.
2. MATERIALS AND METHODS
2.1 EEG recordings
Recordings were performed in an electrically shielded chamber in 10 voluntary healthy
subjects (18–30 years old). Subjects were seated comfortably in a chair and were asked to remain
still and relax while they did a visual and an auditory oddball paradigm (see below). The EEG data
was recorded continuously using 64 electrodes placed according to the international 10-20 system,
band pass filtered between 0.1 Hz and 250 Hz and sampled at 512 Hz, using an average reference.
After the recording, the EEG signals were re-referenced to the average of the left and right mastoids
and trials that were contaminated with eye blinks were removed manually from each data set. For
each trial, one second pre- and one second post-stimulation were stored for further analysis.
2.2 Visual oddball Paradigm
As in previous studies (1), pattern visual event-related potentials (VEPs) were obtained with a
checkerboard pattern (side length of checks: 50' visual angle). A sequence with two different stimuli
was presented pseudo randomly (N=250 stimuli): the frequent or non-target stimuli were a colour
reversal of checks (80% of the stimuli), while the less frequent or target stimuli were colour reversals
with a half check displacement (both horizontal and vertical) of the pattern (20% of the stimuli).
Subjects were asked to ignore the non-target stimuli and press a key whenever they saw the target
ones. Each pattern reversal was shown for 1 sec and the inter stimulus interval varied pseudorandomly between 2 and 2.2 sec. No two target stimuli appeared in succession. Subjects were asked
to fixate on a small red circle in the centre of the screen during the recording
2.3Auditory oddball paradigm
Auditory event-related potentials (AEP) were obtained with an oddball paradigm, using a
sequence with two different tones: nontarget stimuli (80%) had a frequency 2000 Hz and target
stimuli (20%) a frequency 1000 Hz. Subjects were instructed to press a key whenever they heard the
target tone and ignore the non-target ones. Each stimulus was presented for 100 ms and the inter
stimulus interval varied pseudo randomly between 1.5 and 1.7 sec. As with the VEP, subjects were

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asked to gaze on a small red circle in the centre of the screen during the recording to avoid eye
movements.
2.4 Synthetic data
To evaluate the performance of the proposed algorithm, as in previous works (9), the typical
ERP components obtained with a visual oddball, the P1, N2 and P3, were simulated using three
Gaussian functions added to background EEG activity (Fig. 1). Random fluctuations in the latency of
the simulated components were introduced in order to resemble the latency variability across
single trials (ranges, P1: 90–125 ms, N2: 120–155 ms and P3: 400–700 ms). The background EEG
activity was taken from the recording of one subject with eyes open fixating on a red circle in the
centre of the screen. Thirty single trials of the noisy ERPs, 2 sec each, were generated with different
signal to noise ratios (SNR). The SNR was defined as the ratio between the standard deviations of
the simulated ERPs and the one of the background EEG activity.
2.4 Wavelet denoising
Wavelet transform
The wavelet transform is the inner product of a signal with dilated and translated versions of a
wavelet function (Mallat, 1999). Given a signal x(t) and a wavelet function ψa,b(t) the continuous
wavelet transform (CWT) is defined as:
Wψ X (a, b ) = X ,ψ a ,b ,

…. (1)

t −b
,
 a 

….(2)

ψ a ,b = a

−1 / 2

ψ

where a, b∈ ℜ are the scale and translation parameters, respectively.

Fig 1: (A) Average Simulated with(gray) and without(Black) the background “noisy” EEG activity
SNR1 ( b) First 5 out 30 simulated single trails
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Fig 2: Wavelet decomposition and denosing of Donoho’s method and NZT

3. PROBLEM STATEMENT
3.1 Dononho’s denoising implementation: The ERP signals contain a mixture of ongoing EEG
background activity and evoked potentials. For the purpose of denoising the data, we will consider
the former as the noise to be removed (although by no means we argue that the background EEG is
just noise) and the latter as the signal of interest to be extracted. Using the wavelet formalism,
Donoho and colleges proposed a denoising implementation where, in each scale, the wavelet
coefficients are selected by thresholding (Donoho, 1993; Donoho and Johnstone, 1994b; Johnstone
and Silverman, 1997). Following this approach, for each scale j a threshold Tj is defined as:
T j = σ j 2 log e N

….(3)

Where N is the number of wavelet coefficients and
deviation of the noise for each scale.

σj

=Median

{

X j ,1 − X j , X j ,2 − X j ,........,X j ,k − X j

}/ 0.6745

σj

is an estimation of the standard

....(4)

Denoising is done by hard thresholding the coefficients of each scale as follows

X ( j, k ) if X

j ,k

>Tj

X den ( j , k ) =
0 if

X

j ,k

≤ Tj

....(5)

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The denoised average ERP is then obtained by doing a wavelet reconstruction from the
denoised coefficients. Then, this same set of coefficients can be used to denoise the single trial data.
The rationale of this procedure is that one in principle expects to find the single-trial evoked activity
in the same time and frequency ranges of the average evoked responses. However, it should be noted
that this does not necessarily need to be the case. For example, there could be some latency jitter in
the single trials that may lead to broader peaks (i.e. lower frequency composition) in the average
responses.
3.2 NZT Denoising: Using Donoho's implementation we found that it is not always possible to
separate the ERP from the background EEG (see Fig. 2). The problem is that with Donoho's method
each wavelet coefficient is considered individually, irrespective of the value of other neighboring
coefficients at the same or at the next scales, whereas the patterns of a signal are typically distributed
across a set of nearby coefficients; in other words no pattern is localized at one and only one
coefficient. It has been proposed that considering the value of nearby coefficients can improve
denoising results. Our proposed algorithm thus combines two such improvements: the first one is to
decide whether each coefficient should be kept or not based not only on its value but also on the
value of its closest neighbors in the same scale and the second one is to also use information from the
decomposition at the higher scales, what is known as Zerotrees denoising.
X den ( j , k ) =

X ( j, k ) if X

2

j,k −1

+ X2 j,k + X2 j,k+1 > T2 j

0 if X2 j,k−1 + X2 j,k + X2 j,k+1 ≤ T2 j
….(6)
Following Cai and Silverman the threshold for each scale was defined as:
T 2 j = σ 2 j (2 log e N ),

….(7)

Where σ j was estimated as in equation (4).
3.3Denoising of ERPs
Compared to the denoising implementations described above, in our case we introduced two
modifications for the analysis of ERP signals. First, for the estimation of the thresholds in Eq. (3) and
Eq. (7) we used only baseline coefficients (i.e. before stimulus onset). Second, instead of the total
number of wavelet coefficients (N), in both equations we used the number of coefficients in each
scale (K), which gave better results. Fig. 2 shows the 5 level decomposition of an average visual
ERP, and its denoising using Donoho's and the NZT denoising methods. With Donoho's method,
each coefficient is considered independently, which, as shown in the figure, it does not give an
optimal removal of the baseline and a reconstruction of the ERP responses. For example, the
coefficients in level D5 and A5 highlighted in black correlate with the P1–N2 components, but they
are relatively small and are deleted with Donoho's method, thus affecting the shape of these ERP
responses. On the contrary, based on the values of neighboring coefficients and its “parent”, these
coefficients are kept by the NZT method and the reconstruction of the average ERP looks more
accurate. Analogously, the baseline coefficient in D5 marked in gray is relatively large and it is not
deleted by Donoho's method, thus introducing some baseline fluctuations. Given the value of its
neighbors in the same scale and its parent in level A5, this coefficient deleted with the NZT method
— thus improving the denoising outcome. The performance of these two methods are quantified and
compared with synthetic data in the next sections.

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4. PROPOSED ALGORITHM
4.1 Empirical Mode Decomposition
Empirical mode decomposition is an adaptive method designed to unmix a non-linear and
non-stationary signal s(n) in a set of intrinsic modal functions (IMFs), each one containing a
spectrally independent oscillatory mode [5]. They must satisfy two conditions: 1) the number of
extrema and zero-crossing must be equal or differ at most by one, and 2) the mean value of the upper
and lower envelopes must be
zero. IMF extraction, known as sifting process, is described as follows:
1. Find local minima and maxima of s(n).
2. Form upper, eu(n), and lower, el(n), envelopes by cubic splines interpolation.
3. Find the mean, m(n) = eu(n)+el(n)/ 2 .
4. If h(n) = s(n)−m(n) is not an IMF, go to step 1 using h(n) instead if s(n). Else, h(n) = IMF1(n).
5. If the residue, r1(n) = s(n)−IMF1(n) has more than a zero cross, go to step 1 and find next IMF.
Once IMFk(n) are extracted, the signal can be expressed as:
M

s ( n) = ∑ IMFk ( n) + r ( n)

….(8)

k =1

4.2 Clear Iterative interval-thresholding method
To enhance the performance compared to EMD-IIT, the denoising can be achieved with a
variant called clear iterative interval-thresholding (EMD-CIIT). The need for such a modification
comes from the fact that the first IMF, especially when the signal SNR is high, is likely to contain
some signal portions as well. If this is the case, then by randomly altering its sample positions, the
information signal carried on the first IMF will spread out contaminating the rest of the signal along
its length. In such an unfortunate situation, the denoising performance will decline.
In order to bypass this disadvantage of EMD-IIT it is not the first IMF that is altered directly
but the first IMF after having all the parts of the useful information signal that it contains removed.
The “‘extraction” of the information signal from the first IMF can be realized with any thresholding
method, either EMD-based or wavelet based. It is important to note that any useful signal resulting
from the thresholding operation of the first IMF has to be summed with the partial reconstruction of
the last L−1 IMFs. More specifically, the steps2 and 3 of EMD-IIT have to be replaced with the
following 5 steps:
1) Perform an EMD expansion of the original noisy signal x.
2) Perform a thresholding operation to the first IMF of x(t) to obtain a denoised version ˜h(1)(t) of
h(1)(t).
3) Compute the actual noise signal that existed in h(1)(t), h(1)n (t)=h(1)(t) −˜h(1)(t)
4) Perform a partial reconstruction using the last L − 1 IMFs plus the information signal contained in
the first IMF, xp(t) = ∑ h(i)(t) +˜h(1)(t).
5) Randomly alter the sample positions of the noise-only part of the first IMF,

h(1)a (t) = ALTER(h(1)n (t)).
The effectiveness of the subtraction from the first IMF of any existing information signal For
the first IMF denoising (see step 2 above), Bayesian wavelet thresholding was used. In fact, in all the
cases we have tested, the EMD interval thresholding performed similarly or worse than the Bayesian
wavelet denoising when it came to the denoising of the first IMF. As a result, hereafter, whenever the

408


EMD-CIIT is used, the adoption of the Bayesian method for the extraction of the useful signal from
the first IMF is implied unless the use of a different method is explicitly mentioned.
5. RESULTS
To quantify denoising performance, we applied the NZT method to the simulated ERPs and
compared its results with those obtained with the standard denoising implementation by Donoho.
Compared to the original signals, with NZT denoising we had a general improvement in the
extraction of P1 amplitude and latency (except for the P1 latency with SNR=0.5). On the contrary, in
most cases Donoho's implementation gave errors that were larger than the ones obtained with the
original signal. For all SNRs the estimation of the single trial N2 amplitudes
was significantly (P<0.05) improved by the NZT compared to the original data, while differences
with Donoho's method were not significant. Both denoising methods improved the N2 latency
estimation, except for SNR=0.5, where Donoho's method gave a much larger error than NZT and the
original signal. Furthermore, both denoising methods significantly improved the estimation of the
single-trial P3 amplitudes (P<0.001) compared to the original data. In general, NZT also gave the
best estimation of the single trial latency of the P3.
The figures shows the mean percentage improvement in the estimation of the single trial
amplitudes and latencies with Donoho and NZT, averaging across ERP components and SNRs. With
the NZT the improvement in the single trial amplitude and latency estimations was significantly
larger than zero (P<0.001, t-test). Compared to Donoho's method, NZT gave a better estimation of
the amplitudes and latencies of the single trial ERPs (and this difference was highly significant, with
P<0.001 for the amplitude estimations).
Altogether, NZT denoising significantly improved the estimation of the amplitude and
latency of the single trial ERP components and
gave a lower RMS error compared to the original (not denoised) signals. The performance of
Donoho's method was in general poorer than the one with NZT.

Wavelet-5levels
5

raw
wavelet denoised

4

A m p lit u d e (u V )

3
2
1
0
-1
-2
-3

0

0.1

0.2

0.3

0.4

0.5 0.6
time(s)

0.7

0.8

0.9

1

Fig 5.1. Comparison of original signal and wavelet denoised signal

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EMD-5 Hz
5

raw
EMD denoised

4
3

A m p litud e(uV )

2
1
0
-1
-2
-3

0

0.1

0.2

0.3

0.4

0.5
0.6
time(s)

0.7

0.8

0.9

1

Fig 5.2. Comparison of original signal and EMD denoised signal

Comparison of denoised averages
6

Raw average
EMD
Wavelets

5

Am plitude (uV)

4
3
2
1
0
-1
-2
0

0.5

1

1.5

Time(s)

Fig 5.3. Comparison of original signal and EMD, wavelet denoised signals

To start with, the effect on the denoising performance of either adopting fixed or sifting
dependent IMF energy curves with respect to the number of sifting iterations is studied in 5.3 More
specifically, the adopted performance measure is the SNR after denoising when the SNR before
denoising is either and the signals used are the Piece-wise regular and the Doppler signal both
sampled with sampling frequency that result in 2048 samples. The results shown iterations. These
results have been evaluated with other regular and irregular signals.

410


SNR Calculation
Signal-to-noise ratio is defined as the power ratio between a signal (meaningful information)
and the background noise (unwanted signal):

 Psignal 
 = Psignal , dB − Pnoise,dB
SNRdB = 10 log 10 
P

 noise 
Amplitude Deviation
AD= Abservedamplitude − Actualamplitude
Latency deviation
LD= Abservedlatency − Actuallatency
The SNR values as follows for DONHO, NZT and EMD
Performance measures
Table 1
Wavelets

EMD

Noise reduction (%)

43

52

SNR improvement (%)

32

44

Signal loss (%)

1

0

Amplitude deviation
Wavelets: 1.80
EMD: 1.42
Latency deviation
Wavelets: 0.0705
EMD: 0.0701
6. CONCLUSION
In this paper we presented an automatic method to denoise single trial evoked responses.
The method is based on the wavelet transform and uses the inter- and intra-scale variability of the
wavelet coefficients to select those that deviate from baseline values. We quantified its performance
with simulated data resembling real evoked responses, and showed a significant improvement in the
estimation of the single trial evoked traces, as well as on the estimation of the single trial amplitudes
and latencies of 3 different ERPs. With real data, although we cannot quantify results due to the lack
of ‘ground truth’, we showed a clear improvement in the identification of the evoked responses by
using EMD. This method allows the study of single-trial evoked responses and how these correlate
with different sensory and cognitive processes.

411


7. REFERENCES
[1]
[2]

[3]
[4]
[5]
[6]
[7]
[8]

[9]
[10]
[11]

[12]
[13]
[14]

[15]
[16]
[17]
[18]
[19]
[20]

Quian Quiroga, R., Schürmann,M., 1999. Functions and sources of event-related EEG alpha
oscillations studied with the wavelet transform. Clin. Neurophysiol. 110, 643–654.
Donoho, D.L., 1993. Wavelet shrinkage and W.V.D: a 10-minute tour. In: Meyer, Y.,Roques,
S. (Eds.), Progress in wavelet analysis and applications: proceeding of the International
Conference “Wavelets And Applications,” Toulouse, France — June 1992. Edition
Frontieres, France, pp. 109–128.
Donoho, D.L., Johnstone, J.M., 1994a. Ideal spatial adaptation by wavelet shrinkage.
Biometrika 81, 425–455. Donoho, D.L., Johnstone, I.M., 1994b.
Threshold selection for wavelet shrinkage of noisydata. Engineering in Medicine and Biology
Society, 1994
Engineering Advances:New Opportunities for Biomedical Engineers Proceedings of the 16th
Annual International Conference of the IEEE A24-A25, vol.1
Quian Quiroga, R., 2000. Obtaining single stimulus evoked potentials with wavelet
denoising. Phys. D 145, 278–292.
Quian Quiroga, R., Sakowitz, O.W., Basar, E., Schurmann,M., 2001.Wavelet transformin the
analysis of the frequency composition of evoked potentials. Brain Res. Protoc. 8, 16–24.
Quian Quiroga, R., Van Luijtelaar, E.L.J.M., 2002. Habituation and sensitization in rat
auditory evoked potentials: a single-trial analysis with wavelet denoising. Int. J.
Psychophysiol. 43, 141–153.
Quian Quiroga, R., Garcia, H., 2003. Single-trial event-related potentials with wavelet
denoising. Clin. Neurophysiol. 114, 376–390.
Niedermeyer, E., Lopes da Silva, F.H., 2004. Electroencephalography: Basic Principles,
Clinical Applications and Related Fields. Lippincott Williams & Wilkins.
Lopes da Silva, F.H., 2004. Event-related potentials: methodology and quantification. In:
Niedermeyer, E., Lopes da Silva, F.H. (Eds.), Electroencephalography: Basic Principles,
Clinical Applications and Related Fields.Williams andWilkins, Baltimore, pp. 991–1001.
Quian Quiroga, R., Reddy, L., Kreiman, G., Koch, C., Fried, I., 2005. Invariant visual
representation by single neurons in the human brain. Nature 435, 1102.
tienza, M., Cantero, J.L., Quian Quiroga, R., 2005. Precise timing accounts for posttraining
sleep-dependent enhances of the auditory mismatch negativity. NeuroImage 26, 628–634
Eichele, T., Specht, K., Moosmann, M., Jongsma, M.L.A., Quiroga, R.Q., Nordby, H.,
Hugdahl, K., 2005. Assessing the spatiotemporal evolution of neuronal activation with
single-trial event-related potentials and functional MRI. Proc. Natl. Acad. Sci. U. S. A. 102,
17798–17803.
Tracking pattern learning with single-trial event-related potentials. Clin. Neurophysiol. 117,
1957–1973.
Quian Quiroga, R., Reddy, L., Kreiman, G., Koch, C., Fried, I., 2005. Invariant visual
representation by single neurons in the human brain. Nature 435, 1102.
Jongsma, M.L.A., Eichele, T., Van Rijn, C.M., Coenen, A.M.L., Hugdahl, K., Nordby,
H.,Quiroga, R.Q., 2006.
Quian Quiroga, R., 2006. Evoked Potentials. In: Webster, J.G. (Ed.), Encyclopedia of
medical devices and instrumentation. John Wiley & Sons, pp. 233–246.
Quian Quiroga, R., Atienza, M., Cantero, J.L., Jongsma, M.L.A., 2007. What can we learn
from single-trial event-related potentials? Chaos Complex. Lett. 2, 345–363.
Quian Quiroga, R., Kreiman, G., Koch, C., Fried, I., 2008. Sparse but not ‘grandmothercell’
coding in the medial temporal lobe. Trends Cogn. Sci. 12, 87–91.

412


[21] Wang, Z., Maier, A., Leopold, D.A., Logothetis, N.K., Liang, H., 2007. Single-trial evoked
potential estimation using wavelets. Comput. Biol. Med. 37, 463–473.
[22] Maryam Ahmadi, Rodrigo Quian Quiroga, Automatic denoising of single-trial evoked
potentials, NeuroImage 66 (2013) 672–680.
[23] Darshana Mistry and Asim Banerjee, “Discrete Wavelet Transform using Matlab”,
International Journal of Computer Engineering & Technology (IJCET), Volume 4, Issue 2,
2013, pp. 252 - 259, ISSN Print: 0976 – 6367, ISSN Online: 0976 – 6375.
[24] G. Hemalatha, Dr.B. Anuradha and V. Adinarayana Reddy, “Efficient Extraction of Evoked
Potentials from Noisy Background EEG”, International Journal of Electronics and
Communication Engineering & Technology (IJECET), Volume 4, Issue 1, 2013,
pp. 216 - 229, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472.

ABOUT THE AUTHOR

G. Hema Latha received her B.Tech. Degree in Electronics and
Communication Engineering from Sri Venkateswara University, Tirupati in
1997, and M.Tech in Instrumentation and Control Systems from Sri
Venkateswara Unversity, Tirupati in 2003. Smt. Hemalatha joined faculty in
Electronics and Communication Engineering at G. Pulla Reddy Engineering
College, Kurnool. At present, she is working as Associate Professor in
Electronics and Communication Engineering, KSRM College of Engineering,
Cuddapah. Her research interests include Biomedical Signal Processing and
Communication Systems.

Dr. B. Anuradha received her B.Tech. Degree from Gulbarga University,
and M.Tech and Ph.D. degrees from Sri Venkateswara University, Tirupati. She
joined as faculty in Dept. of ECE at Sri Venkateswara University college of
Engineering, Tirupati, India in 1992. She is now working as a Professor since
2009. She guided many B.Tech and M.Tech projects. At present SIX research
scholars are working for Ph.D. She had a good number of publications in various
international journals.

V. Adinarayana Reddy received his graduate degree in Electronics and
Telecommunication Engineering from The Institution of Electronics and
Telecommunication Engineers, New Delhi in1996 and M. Tech in Electronic
Instrumentation and Communication Systems from Sri Venkateswara University,
Tirupati in 1999. He joined as faculty in the Department of Electronics and
Communication Engineering at KSRM College of Engineering, Cuddapah,
worked as Professor and Head of the Department, Electronics and
Communication Engineering at Rajoli Veera Reddy Padmaja Engineering
College for Women, Cuddapah. At present he is working as Professor of ECE at
G. Pulla Reddy Engineering College, Kurnool. His research area of interest
includes signal processing and communication systems.

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