SIMULATION OF OFDM MODULATION ADAPTED TO THE TRANSMISSION OF A FIXED IMAGE

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SIMULATION OF OFDM MODULATION ADAPTED TO THE TRANSMISSION OF A FIXED IMAGE Powered By Docstoc
					        INTERNATIONAL and Communication Engineering & Technology (IJECET),
 International Journal of Electronics JOURNAL OF ELECTRONICS AND
 ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

 ISSN 0976 – 6464(Print)
 ISSN 0976 – 6472(Online)                                                 IJECET
 Volume 4, Issue 3, May – June, 2013, pp. 162-176
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        SIMULATION OF OFDM MODULATION ADAPTED TO THE
      TRANSMISSION OF A FIXED IMAGE ON DISTURBED CHANNEL

                     Louis Paul Ofamo Babaga, Ntsama Eloundou Pascal
       Physics Department, Faculty of Sciences/ University of Ngaoundere, P. O; Box 454
                                   Ngaoundere, Cameroon


 ABSTRACT

         In recent years, the speed in the transmission of audio and video data is a major
 concern. Thus, in this paper we present the results of the modulated OFDM (Orthogonal
 Frequency Division Multiplexing) still images that is based on the fast Fourier transform
 (FFT: Fast Fourier Transform) digital transmission. These results are obtained from a chain
 of communication developed in MATLAB. We evaluate the performance of the transmission
 system in terms of visual quality of the image reception (98% of the original image). We also
 obtain the different values of SNR, TEB, and other important parameters relying on the
 classic OFDM with a guard interval of time corresponding to 25% of the useful symbol
 period, and the modified OFDM, by just reducing that interval. The results are presented
 according to three patterns of M-PSK modulation frequency used in simulation. Namely:
 BPSK, QPSK and 16PSK and by extension, 256PSK modulation. It should be noted that
 convolutional coding is used to improve transmission quality.

 Keywords: Digital transmission, Orthogonal Frequency Division Multiplexing (OFDM),
 FFT, cyclic time guard.

 I.      INTRODUCTION

         Future mobile radio communication systems that can provide diverse transmission
 services such as video, voice, image and other data, with high transmission rate and low
 power transmission, are of great interest. The problem of transmitting high data rates on the
 frequency of a fading channel is inter-symbol interference (ISI), which severely degrades
 system performance. OFDM digital subcarriers in multiple form by the orthogonal frequency
 division transmission, is a solution that can effectively combat ISI [1,2]. OFDM scheme, a bit
 stream is converted to high-speed trains with parallel low bit rate. Parallel streams are
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modulated on orthogonal subcarriers. Spectrum of these subcarriers are closely spaced and
covered with a high efficiency of bandwidth. The bandwidth of these subcarriers is small
compared to the coherence bandwidth of the channel that is the sub-carriers are not subject to
flat fading. OFDM also uses a time guard duty at the beginning of each symbol to remove
any shorter than its length [3] ISI. In this paper, a study on combined use of convolutional
coding and OFDM technique for the transmission of fixed images, simulated with Matlab is
presented in four modulation formats (BPSK, QPSK, 16PSK and 256PSK). Thus, we propose
a new division of time Guard in OFDM system (below 25% of a useful symbol period). This
system will provide better picture quality reception. The paper is organized as follows:
Section 2 provides background information on the OFDM modeling classic system, Section 3
presents the OFDM implemented modulator, Section 4 presents the disturbed channel, the
overview of the demodulation is given in Section 5, and the results are given in Section 6.

II.    OFDM MODELING

        OFDM is a combination of modulation and multiplexing. We use DPSK modulation.
In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to
each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier
guard bands are not required. According [4], in an OFDM system, the carrier spacing 1/NT is
  f, where N is the number of carriers, and 1/T is the symbol rate [5]. With this carrier
spacing, sub-channels can maintain orthogonality, although they overlap. Therefore, there is
no inter-carrier interference (ICI) with ideal OFDM systems. The transmitted signal through
the system for an OFDM symbol period is of following form:

                                                    
               s (t ) = Re ∑ an h(t )e j 2π f nt +φ                                     (1)
                           n                        

        Where an is the data symbol transmitted on the n-th subcarrier, h(t) is the pulse
shaping filter response.
        fn is the n-th subcarrier frequency fn = f + N∆f.
        As the number of OFDM subcarriers increases, the complexity of the modulator and
demodulator is increased accordingly. However, the OFDM modulator and the demodulator
can be implemented easily by use of inverse discrete Fourier transform (IDFT) and discrete
Fourier transform (DFT), respectively. In practice, the couple IFFT/FFT (fast Fourier
transforms inverse and direct) is used for its efficiency and speed.
        The time-domain coefficients Cm can be calculated by:

                              N −1          2π nm
                         1             −j
               Cm =
                         N
                              ∑ an e
                              n =0
                                              N
                                                                                          (2)


       Where an is the input to the IDFT block which is the data symbol for n-th subcarrier.
       Cm is the m-th output of IDFT block. After this operation, the parallel output of IDFT
block Cm (m = 1, …, N - 1) is converted into a serial data stream. Figure 1 shows a block
diagram of the OFDM transmitter. In equation (2), the data symbols of the frequency domain
are converted to a series of samples in the time domain.

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                                                       OFDM modulator

                                                               DPSK
     Binary input     Convolutional        Serial                                  IFFT        Cyclic        Parallel
                                                           Modulation
     data (image)       encoder             to                                    (IDFT)     extension         to
                                                           (1, 2, 4 or 8
                                          Parallel             bits)                          addition        Serial



                                                                                                                  Communication
                                                                                                     Noise           channel



                                                              DPSK
      Binary        Convolutional      Parallel         Demodulation                FFT        Cyclic         Serial
   output data        decoder            to            (1, 2, 4 or 8 bits)         (DFT)     extension         to
     (image)                            Serial                                                removal        Parallel

                                                                                  OFDM demodulator




                          Figure 1. OFDM transmission and reception scheme

         * Preservation of orthogonality (Guard Interval)
         Following the same symbol arriving at a receiver by two paths will add causing two
types of defects:
  • The intra symbol interference: addition of a symbol with itself slightly out of phase.
  • The inter symbol interference: adding a symbol with the following over the preceding
       slightly out of phase.
         Between each transmitted symbol, inserting a guard interval called "dead zone". In
addition, the useful symbol duration is greater than the spread echoes. These two precautions
will limit the inter-symbol interference. The time you issue differs from the information
symbol period because it must take into account relevant periods between a "call time",
which aims to eliminate the ISI continues despite the carrier orthogonality. Between the
symbol periods (Ts), the useful (Tu) and the guard interval (Tg), therefore establish the
relationship:
                 Ts = Tu + Tg                                                              (3)

                                           Guard period         IFFT output

                                                  Tg                         Tu
                                                                 Ts



                                    Figure. 2. Time guard interval (cyclic prefix)

        Figure 2 shows the addition of a guard interval. The symbol period is extended so as
to be greater than the integration period Tu. All carriers are cyclical inside you; it is the same
for the entire modulated signal. The length of the interval is selected to match the expected
level of multipath. It should not be too much of you, not to sacrifice too much data capacity
(and spectral efficiency). For DAB (Digital Audio Broadcasting), a guard about you Tu/4 is

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   used; DVB (Digital Video Broadcasting) has more options, the largest being Tu/4 where
   OFDM modified guard interval ≤ Tu/4; we also simulated and compared with the results for
   Tg=Tu/4.
           At the receiver, the signal is converted to base band and sampled at the symbol rate
   1/T. Then, N serial samples are converted to parallel data and passed to a DFT which
   converts the signal from time domain to frequency domain. To decrease the SNR required to
   achieve the required quality of the received image, a convolutional coding [5, 6, 7] is applied
   to the OFDM system. OFDM coding is the concatenation of the OFDM system with
   convolutional encoding. As seen, the convolutional coding is integrated into the OFDM
   system to improve the performance in noisy channels [5, 8]. The binary input information are
   first encoded using any encoding of convolutional code rate, then, they are modulated and
   transmitted through a channel with additive noise. In this model consider frequency selective
   time varying fading channel with additive noise, where the channel impulse response can be
   represented by the formula:

                                  L
                            1
                  h(t ) =
                             L
                                 ∑ e (θ
                                 m =1
                                        j   m + 2π f Dm t   )
                                                            δ (t −τ m )                      (4)


          Where L is the number of reflected multipaths, τm is the delay, θm is the phase rotation
   and fDm is the Doppler frequency offset of the mth path.

III.      OFDM MODULATION

           Conventional OFDM can be modified by adjusting certain sensitive parameters and/or
   adding new elements that can improve the system. Thus, conventional time guard 25% of
   symbol period can be reduced to a reasonable value to avoid inter-symbol interference. In the
   classic OFDM, we could associate a convolutional coding to improve the visual quality of the
   image reception (See figure 1)

   3.1 Convolutional coding
          According [4], simulation studies have been performed using convolutional coding
   with OFDM systems considered in figure 1. The parameters of the convolution coding are
   code rate (r) equal 1/2 and 1/3 with constraint lengths (K) equal 3 and 7 for each of them. For
   rate 1/2 the function generators are [6,7] for constraint length 3 and [133,171] for the
   constraint length 7, while for rate 1/3 are [6,7,7] for the constraint length 3, and
   [133,145,175] for the constraint length 7. All these generator vectors are represented in octal
   form.

   3.2 Type of OFDM modulation implemented
          The flow of serial input data to be converted in parallel, the modulator has to add a
   number of zeros at the end of the data stream in order to adapt the data flow to enter a 2-D
   matrix [9]. Suppose a frame of data with 11530 symbols is being transmitted by 400 carriers
   with a capacity of 30 symbols/carrier, 470 zeros are padded at the end in order for the data
   stream to form a 30-by-400 matrix, as shown in Figure 3. Each column in the 2-D matrix
   represents a carrier while each row represents one symbol period over all carriers.


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                                            400
                                  30
                                             Data


                             Figure 3. Data transmission matrix

3.2.1 Differential Phase Shift Keying (DPSK) modulation
        The DPSK Baseband Modulator block modulates the signal using the differential
phase shift keying method. The output is a baseband representation of the modulated signal.
        Before, differential encoding can be operated on each carrier (column of the matrix),
an extra row of reference data must be added on top of the matrix [10]. The modulator creates
a row of uniformly random numbers within an interval defined by the symbol size (order of
PSK chosen) and patches it on the top of the matrix. Figure 4 shows a 31 by 400 resulted
matrix.

                                                  400
                                            Reference Row
                                       31         Data




                               Figure 4. Differentiated matrix

       For each column, starting from the second row (the first actual data symbol), the value
is changed to the remainder of the sum of its previous row and itself over the symbol size
(power 2 of the PSK order).
       Figure 5 show the signal modulated on a carrier; modulated in a symbol period. The
DPSK modulator generates a matrix filled with complex number whose phases are translated
into small amplitudes [11]. These complex numbers are then converted into a rectangular
shape for further processing. The BPSK (symbol size is 2), 16PSK (symbol size is 24) and
256PSK (28) just follow the same principle.




               Figure 5. OFDM time signal (one symbol period in one carrier)


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3.2.2 Bloc of Inverse Fast Fourier Transform
       For a vector of length N, direct and inverse Fast Fourier transforms are given by
formulas (5) and (6):

                                           N
                       X ( k ) = ∑ x ( j )wNj −1)( k −1)
                                           (
                                                                                          (5)
                                           j =1



                                       N
                                   1
                    x( j) =
                                   N
                                       ∑ X ( k )w (
                                       k =1
                                                         − j −1)( k −1)
                                                         N                                6)



                           2π i
                       −
       With   wN = e        N



       Figure 6, shows an enlarged to a certain size of the IFFT matrix (e.g. size of the IFFT
= 1024) and becomes a matrix 31×1024. Since each column of the matrix represents a DPSK
support, their values are stored in the columns of the matrix where the IFFT their
corresponding carriers should reside. Their combined values are stored in the columns
corresponding to the locations of carriers combined.

                                                              1024

                                                                    Data
                                  31
                                                  Data            conjugate

                                                  400              400


                                               Figure 6. IFFT matrix

       All other columns in the IFFT matrix are set to zero. The matrix for signal
transmission, Inverse Fast Fourier Transform (IFFT), and only the real part of the result is
valuable, so that the imaginary part is eliminated [12].

3.2.3 Insert periodic time guard
        An exact copy of the last portion of 25% of each symbol period (row of the matrix) is
inserted at the beginning of the classic OFDM [13, 14]. The time of periodic care, is
synchronization to the receiver for each symbol period demodulation signal reception [7].
The guard time is changed during the simulation. Modified OFDM has a guard interval of
20% of symbol period;
        Figure 7 shows a time domain representation of an OFDM Signal. Figure (7.a) shows
a time domain representation of the conventional OFMD signal, where the guard period is
fixes during all the frame of the data file of the image. Figure (7.b) shows a time domain
representation of the new guard period where, Tg ≥ Tgm et Tu ≥ Tum

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                                                Copy


                                 Guard Period                           Guard Period
                a)
                         IFFT                    IFFT output                           IFFT

                                 Tg                     Tu
                 Symbol                                                            Symbol
                 N-1                                                               N+1
                                                    Ts

                                                 Symbol N




                                                    Copy


                                   Guard                                  Guard
                 b)
                          IFFT    Period         IFFT output              Period


                                 Tgm                              Tuu
                      Symbol                                                Symbol
                       N-1                                   TS             N+1

                                                       Symbol N


                        Figure.7. Integration of the signal with guard interval

        The matrix becomes a matrix of modulation when converted to serial. A time-
  modulated in a data frame signal is generated.

IV.      COMMUNICATION CHANNEL

         Two properties of a typical communication channel are modelled. First, a variable
  clipping (off peak power) to MATLAB program is set by the user. The root mean square
  powers of the transmitted (RMSP) before and after the channel signal are indicated.
  Secondly, the channel noise is modeled by adding white Gaussian noise (AWGN) defines by:

                          var iance of the mod ulated signal
                 σ=                                                                           (7)
                                      linear SNR


                                                SNRdB

          With linear SNR = 10
                                                 10

          It has a mean of zero and a standard deviation equaling the square root of the quotient
  of the variance of the signal over the linear Signal-to-Noise Ratio, the dB value of which is
  set by the user as well.



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V.       OFDM DEMODULATION

          The DPSK Baseband Demodulator block demodulates a signal that was modulated
  using the differential phase shift keying method. The input is a baseband representation of the
  modulated signal. The input must be a discrete-time complex signal. The input can be either a
  scalar or a frame-based column vector.
          As any type of modulation/demodulation, the OFDM demodulation process is
  essentially an inverse of the OFDM modulation. And as the modulator, the OFDM
  demodulator demodulates the received data frame with respect to the transmitted image
  unless the data have a length less than the total number of symbols per frame designed [15].
           For remove a periodic time guard, the previous example used in section 3.2 should
  continue to be used for illustrative purposes. Figure 8 shows that after converting a frame of
  discrete time signal from serial to parallel, a length of 25% of a symbol period is discarded
  from all rows. Thus the remaining is then a number of discrete signals with the length of one
  symbol period lined up in parallel.
                                   1280
                                    400                               1024
                                                                       400

                          31
                          30                             31
                                                         30
                                     Data
                                     Data                              Data
                                                                       Data



                                  Figure 8. Time Guard Removal

VI.      SIMULATION RESULTS

          The performance evaluation is done by measuring the quality of the received image.
  There are two ways to measure quality image: subjective based and objective based. The root
  mean square error (RMSE) and SNR are the most commonly objective based measure used
  due to their simplicity and ease of calculation.
          Root mean square error between the original and reconstructed image frame defined
  by:

                               M −1 N −1
                        1
                               ∑ ∑ ( g ( x , y ) − f ( x, y ) )
                                                                  2
          RMSE =                                                                            (8)
                      M ×N     x =0 y =0


         Where f(x,y) is the original image frame
         g(x,y) is the reconstructed image frame after the decompression process.
         M x N is dimensions of image frame
         In this paper objective and subjective criteria are used.
         The different values of BER (Bit Error Rate) and other parameters are presented in
  terms of four modulation formats used in the simulation. Namely: BPSK, QPSK, 16-PSK and
  256-PSK. The performances of conventional OFDM system are evaluated by the following
  parameters:
    • Root Mean Square Power at the input of transmission channel (RMSPi), define by:



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                        1 −τs
                        e if τ ≥ 0
               RMSPi =  s                                                         (9)
                       0      other
                       
  •   Root Mean square Power at the output of transmission channel (RMSPo), define by:
                       
                                        2
                                (τ −τ )
                         1
                              −
                                 2 s2
              RMSPo =  2π s e         si τ ≥ 0                             (10)
                        
                        0            other
       Where s is the RMS delay (root mean square) transmission.
       τ is the average delay introduced by the noisy channel and τ is the delay in the
entrance channel.
  • Bit Error Rate define by:
                                    1
                 BERBPSK, QPSK =
                                    2
                                      erfc   (   SNRdB   )                         (11)


       The simulation is performed for two cases: the classical OFDM and modified OFDM.
Simulation results are presented through the measurement of the quality of picture. The
simulation parameters chosen are shown in Table 1.

                              Table1. Parameters of simulation
                           Parameters                Values
                          Source Image              256x256
                               Size
                            IFFT size                 2048
                           Number of                  1009
                             Carriers
                           Modulation      BPSK, QPSK, 16PSK or
                             Method                 256PSK
                           Peak Power                10 dB
                             Clipping
                         Signal-to-Noise          [0….25] dB
                              Ratio

        Information in table 1 can be modified depending on the configuration of OFDM
system desired. The size of IFFT is 2048 and offers a channel bandwidth wide (20 MHz).
        Table 2 shows input images for four modulation formats and guard interval of 25% of
useful symbol period. We observe that, for a SNR of 25 dB, reconstructed images are almost
identical to the original image for BPSK and QPSK. For 16PSK and 256PSK modulations,
the reconstructed images are noisy.
        A table 3, 4 and 5 shows the variation of different parameters. We find that the values
of RMSPo are less than the RMSPi. For BPSK modulation, the BER is much reduced.
        For BPSK modulation with a SNR 25 dB, the quality of reconstructed image is
95.8%.


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        Table 6 shows the results of the modified OFDM. For OFDM modified, the image
quality improves with SNR smaller and guard intervals of 20% of a useful symbol period.
With a convolutional code rate of 1/3, a guard interval of 20% and a SNR of 16dB, received
image are identical to the original image.

 Table 2. OFDM simulated classic transmission, original and received images with a guard
          time of 25% of the useful symbol period (without convolutional coding)

     Original
   image

                       Received          Received           Received           Received
                     image             image              image              image
                       SNR = 0dB         SNR = 5dB          SNR = 10dB         SNR = 25dB



     BPSK
   modulation
      with guard
   time
      interval
   25%


     QPSK
   modulation
     with guard
   time
      interval
   25%


     16PSK
   modulation
      with guard
   time
      interval
   25%


   256PSK
   modulation
     with guard
   time
     interval 25%


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                          Table 3. Numerical results for a BPSK
               SNR        RMSPi      RMSPo           BER       Image quality
               (dB)        (dB)        (dB)           (%)          (%)

                 0         15.32          13.34        17.31          23.00

                 5         14.75          11.86         2.03          84.91

                10         15.11          10.95         0.16          91.50

                25         17.30          9.10        0.00001         95.80



                           Table 4. Numerical results for a QPSK
               SNR         RMSPi       RMSPo          BER      Image quality
               (dB)         (dB)        (dB)           (%)         (%)

                 0          14.02         13.02        46.31           8.38
                 5          14.61         11.91        18.85          43.91
                10          14.35         10.09        2.28           91.22
                25          14.61          7.16       0.0001          93.80



                           Table 5. Numerical results for a 16PSK
                SNR        RMSPi       RMSPo           BER      Image quality
                (dB)        (dB)        (dB)           (%)          (%)


                 0          15.18         13.33        84.86          2.32

                 5            16          12.74        72.61          7.56

                 10         14.03          10.3        56.39          19.16

                 25         15.18          7.53         9.59          81.75



      Table 6 clearly shows that changing the guard interval keeps below 25% of the
symbol period; we get sharper images with SNR lower than those used by conventional
OFDM.




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  Table 6. Modified OFDM: performances of image transmission with guard time intervals
                       equal to 20% and a convolutional coding

          Original Image




                       SNR        guard              image
                       (dB)       Interval           Quality     Image received
                                  modified (%)       (%)

         Uncoded
         OFDM
          (QPSK)        19.00          20.00            97.05




           Coded
          OFDM          17.00          20.00            97.90
           r=1/2
          (QPSK)


           Coded
          OFDM          16.00          20.00            98.90
           r=1/3
          (QPSK)



        Table 7 shows a comparison between conventional OFDM and modified OFDM. For
a QPSK modulation format, comparisons show that the addition of a convolutional coding,
and the modified of time guard of 25% to 20% of useful symbol period, we obtains
reconstructed images identical to the original image. This shows the improvement of our
system; hence the advantage of our modified OFDM system. The choice of QPSK format for
the comparison is interesting. Table 7 shows the best image quality of modified OFDM for
different values of SNR, to be compared with the results obtained from convolution OFDM.
Compared to the work of [3, 4], obtained results are satisfactory and improved




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     Table 7. Comparison of results between conventional OFDM and OFDM modified

                           conventional OFDM          Modified OFDM


             Received
              image



               SNR                  25 dB                        25 dB
             Type of           QPSK Without                  QPSK Without
            modulation       convolutional coding         convolutional coding
              Guard                  25%                          20%
             interval
           Image quality            94,80%                       96.82%


             Received
              image



               SNR                  20 dB                      20 dB
             Type of            QPSK Without            QPSK With convolutional
            modulation       convolutional coding           coding r =1/2
              Guard                  25%                        20%
             interval
           Image quality            93.50%                       97.90%


             Received
              image



                SNR                  17 dB                        17 dB
             Type of            QPSK Without            QPSK With convolutional
            modulation       convolutional coding           coding r =1/3
              Guard                 25%                         20%
             interval
           Image quality             92.2%                       98.90%




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VII.      CONCLUSIONS

           In this study, we developed a simulation model of the transmission of fixed images in
   a noisy modified by the OFDM channel, using four modulation formats in Matlab. We have
   shown the interest of a guard interval time modification below 25% of the useful symbol
   period in order to recover a high quality signal transmitted. The addition of convolutional
   coding further improves the quality reception. The results obtained using three modulation
   formats (BPSK, QPSK, 16PSK) are acceptable, we get very close to 10-5 % for BPSK bit
   error rate. The simulation consisted in comparing the conventional OFDM transmission
   system (guard time of 25% of useful symbol period), and the modified OFDM with DPSK
   modulation (guard time of 20% of useful symbol period). The modified OFDM provides a
   better quality image than the classic reception system. Here the choice of the QPSK format
   for comparison is very important.
           However, in our future researches, we would to implement this OFDM modulation
   technique with QAM modulation format, and short guard time interval, so as to further clarify
   the received image.

   REFERENCES

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   [3] M. M. Salah, A. A. Elrahman, M. M. Mokhtar, "Performance Enhancement of Image
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International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME

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     ISSN Online: 0976 –6472.




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