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A Low Pass FIR Filter Design Using Particle Swarm Optimization Based Artificial Neural Network

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A Low Pass FIR Filter Design Using Particle Swarm Optimization Based Artificial Neural Network Powered By Docstoc
					    International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 4, November – December 2012                                    ISSN 2278-6856



         A Low Pass FIR Filter Design Using Particle
         Swarm Optimization Based Artificial Neural
                         Network
                               Neha Aggarwal1, Sheenu Thapar2 and Parminder Kaur3
                                                1
                                                 Desh Bhagat Engineering College,
                                                 Mandi Govindgarh, 147301, India
                                           2
                                           Continental Institute of Engineering & Technology,
                                                  Fatehgarh Sahib 140407, India
                                                 3
                                                 Desh Bhagat Engineering college,
                                                 Mandi Govindgarh, 147301, India

Abstract: For the design of Low pass FIR filters complex          of      filter, for example low pass filter, the desired
calculations are required to calculate the filter coefficients.   amplitude and/or phase response and the tolerances (if
Mathematically, by substituting the values of pass band,          any) we are prepared to accept, the sampling frequency
transition width, pass band ripple, stop band attenuation and
                                                                  and the word length of the input data.
sampling frequency in any of the methods like window
method, frequency sampling method or optimal method we
                                                                  (2)Coefficient calculation: At this step, we determine the
can get the values of filter coefficients h(n).                   coefficients of transfer function, H(z), which will satisfy
In this paper a low pass FIR filter has been designed using       the specifications given in 1. Our choice of coefficient
artificial neural network. The optimization of the network has    calculation method will be influenced by several factors,
been done using particle swarm optimization algorithms. The       the most important of which are the critical requirement
proposed approach has been compared with Kaiser window            in step 1
method. The result shows that the filter designed using ANN
                                                                  (3)Realization: This involves converting the transfer
optimized with PSO requires lesser iterations for the
performance goal meeting.                                         function obtained in 2 into suitable filter network or
Keywords: FIR Filter, Kaiser window, ANN, PSO                     structure.
                                                                  (4)Analysis of finite word length effects: Here, we
1. INTRODUCTION                                                   analyze the effects of quantizing the filters coefficients
                                                                  and input data as well as the effect of carrying out the
With the technological evolution, great advances have
                                                                  filtering operation using fixed word lengths on the filter
been made on design techniques for various digital filters.
                                                                  performance.
A filter is essentially a system or network that selectively
                                                                  (5)Implementation: This involves producing the software
changes the wave shape amplitude -frequency and or
                                                                  code and/or hardware and performing the actual filtering.
phase – frequency characteristics of a signal in a desired
                                                                  The criteria is a linear phase response in frequency
manner. A digital filter is a mathematical algorithm
                                                                  domain called phase response (Jin et al., 2006) as shown
implemented in hardware and/or software that operates
                                                                  in figure. Finally, because there is a tradeoff between
on a digital input signal to produce a digital output signal
                                                                  filter complexity and implementation feasibility,
for the purpose of achieving a filtering objective. A
                                                                  complexity and implementation feasibility, complexity is
simplified block diagram of a real-time digital filter, with
                                                                  a performance criteria. Ideal filter characteristics are
analog input and output signals is given in Fig.1.
                                                                  practically unrealizable. There are many methods to
                                                                  design FIR filter which are:-
                                                                  (1) Fourier series method
                                                                  (2) Frequency Sampling method
                                                                  (3) Window method
                                                                  The most of these design techniques suffer from some
           Fig.1: Block diagram of digital filter.
                                                                  kinds of drawback. Some of them could not give optimal
                                                                  design in any sense, some is lacking of generality, some
2. FIR FILTER DESIGN                                              need long computing time, and so on (Bagachi and Mitra,
The design of a digital filter involves five steps:               1996).Kaiser window method has been used because of
(1)Filter Specification: This may include stating the type        the presence of ripple parameter beta.

Volume 1, Issue 4 November - December 2012                                                                         Page 20
    International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 4, November – December 2012                                    ISSN 2278-6856


                                                                 functions, unlike traditional optimization methods. PSO
                                                                 is less susceptible to getting trapped on local optima
                                                                 unlike GA The network has been trained in such a
                                                                 manner so that the error reduces to minimum. The
                                                                 objectives of the present work are divided into the
                                                                 following sections.
                                                                 (1)To prepare the data sheet using different values of
                                                                 filter parameter achieve the filter coefficient.
                                                                 (2)Using ANN a low pass FIR filter has been designed
                                                                 with PSO as the optimization tool, such that its
                                                                 coefficient match with coefficients obtained with window
                                                                 method.




                 Fig.2: Design of digital Filter

3. KAISER WIDOW
Kaiser determined empirically that the value of β need to
achieve a specified value of A is given by
    0.1102  A  8.7                          for A  50
    
                    0.4
  0.5842  A  21  0.07886  A  21       for 21 A  50
    0.0
    
    
                                                for A  21       4. RESULTS
The case β = 0 is the rectangular window for which A =           The network has been trained using Multilayer
21.                                                              Perceptron in which Error Back Propagation Algorithm
Furthermore, to achieve prescribed values of A and df, M         has been specifically used to design Low Pass FIR filter.
must satisfy equations:
     A 8
               1                 for A  21
M   14.36df
      0.922 / df   1           for A  21
    

Finite Impulse response filters (Öner and paper., 1999)
are preferred for their stable and linear phase
characteristics. But due to long impulse response of FIR
filters there will be more hardware complexity. The
design of digital filter means basically finding the values
of filter coefficients so that given filter specification are
achieved the window based design method are exclusively
used for calculating there coefficient. In this paper Kaiser
window is used for this purpose. ANNs have been used
for the design of digital filter with pass band edge
frequency, transition width, pass band ripple, stopband
attenuation, sampling frequency as input parameters. In
this paper a low pass FIR filter has been designed using
artificial neural network. The optimization of the network
has been done using particle swarm optimization. PSO is                Fig. 3: Training of Artificial Neural Network
a flexible, robust population-based stochastic search              4.1  KAISER VS ARTIFICIAL NEURAL
optimization technique with implicit parallelism, which            NETWORK
can easily handle with non-differential objective
                                                                 Input parameters:-Transition width=50Hz, Sampling

Volume 1, Issue 4 November - December 2012                                                                       Page 21
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 4, November – December 2012                                    ISSN 2278-6856


Frequency=1KHz, Pass band Ripple=0.1dB, Filter           been optimized using PSO. The results obtained are
Length=3, Passband=150Hz, Stopband Attenuation =         shown in Fig. 5, 6, 7 & 8.
10.1040dB.




                  Fig.4: Error Graph

                                                                         Fig.6 : Training states




               Fig.5: Performance Plot




                                                           Fig.7: Neural Network Training optimized with PSO


                Fig.6: Regression Plot
                                                         5. CONCLUSION
amount. The Input Data Set taken is TW =52, SF = 1.3 ,
PBR = 0.12, N=4, PBF=151,SBT=9.9413. The ANN has         The present work has illustrated the use of artificial

Volume 1, Issue 4 November - December 2012                                                            Page 22
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 4, November – December 2012                                    ISSN 2278-6856


neural network for the design of low pass FIR filters          [12] Haykins, S. (2003), “Neural Networks – A
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Volume 1, Issue 4 November - December 2012                                                                     Page 23

				
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Description: International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 1, Issue 4, November – December 2012, ISSN 2278-6856, Impact Factor of IJETTCS for year 2012: 2.524