Fir Band Stop Filter Optimization by Improved Particle Swarm Optimization

Neha Malhotra, IJRIT 106 International Journal of Research in Information Technology (IJRIT)

www.ijrit.com ISSN 2001-5569

Fir Band Stop Filter Optimization by Improved Particle Swarm Optimization

1Neha Malhotra, ²Shikha Khanna

1,2

Dept. of ECE, DIET (Kurushetra University), Karnal, Haryana, India [email protected]¹, [email protected]²

ABSTRACT

This paper proposes a novel optimal design of band stop fir filter using ipso. IPSO is improved PSO that proposes a new concept for velocity vector and swarm updating and hence the solution quality is improved. In this design, magnitude response, phase response, SNR transition width stop band attenuation pass band ripple are specified. A comparison of simulation result with the previous results of IPSO makes the proposed result efficient than earlier results for the design of FIR filter.

KEYWORDS: FIR Filter , Band Stop Filter, Parks and McClellan Algorithm, Evolutionary Optimization, GA, PSO.

I.INTRODUCTION

Digital Signal Processing (DSP) is one of the most powerful technologies that are shaping science and engineering in the twenty-first century. Revolutionary changes have already been made in a broad range of fields: communications, medical imaging, radar and sonar, and high fidelity music reproduction, to name just a few. Each of these areas has developed a comprehensive DSP technology, with its own algorithms, mathematics, and specialized techniques. The digital filters are an essential part of DSP. However digital filters are vastly superior in the level of performance. In this work, a type of digital filter i.e., FIR filters is used to separate one band of frequencies from another. The primary attribute of FIR filters is their stability. This is because they are carried out by convolution rather than recursion. FIR filters are linear phase filters both phase delay and group delays are constant in these filters.

II. FILTERSANDDESIGNTECHNIQUES

Filtering is a process by which the frequency spectrum of a signal can be modified, reshaped or manipulated to achieve some desired objectives. These are as under :

1. To eliminate noise this may be contaminated in a signal.

2. To remove signal distortion this may be due to imperfection transmission channel.

3. To resolve the signal into its frequency component.

4. To demodulate the signal this was modulated at the transmitter side.

5. To convert digital signals into analog signals.

III. TYPES OF FILTER

There are two types of filters depending upon the signal used to process as under :

Neha Malhotra, IJRIT 107 (i) ANALOG FILTERS.

(ii) DIGITAL FILTERS.

ANOLOG FILTER

Analog filters are defined as filters in which both input and output are continuous signals.

DIGITAL FILTER

A digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal. In an analog filter, the circuit “directly”

manipulates the input signal. A digital filter system usually consists of an analog-to-digital converter (to sample the input signal), a microprocessor (often a specialized digital signal processor), and a digital-to-analog converter. Software running on the microprocessor can implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC.

Digital filters are defined as a system in which both the input and output signals are discrete time signals.

IV. LITERATURE SURVEY

Arojit Roychowdhury 2013 describes the some of the techniques used to design FIR filters. In the beginning, the windowing method and the frequency sampling methods are discussed in detail with their merits and demerits. Different optimization techniques involved in FIR filter design are also covered, including Rabiner’s method for FIR filter design. These optimization techniques reduce the error caused by frequency sampling technique at the non-sampled frequency points. A brief discussion of some techniques used by filter design packages like Matlab is also included.

Soodabeh darzi,Tiong Sieh kiong,Mohammadrezd Agheai 2012 describes the applications of PSO in Linear Constraint Mean Variance (LCMV) beam forming technique that SNR , data rates ,null steering and coverage of cellular system.

Satyesh Sharan Singh,Mukesh Kumar,Rohini Saxena,Priya 2012 In this paper we are going to survey the application of particle swarm optimization (PSO) in WSN over different type of clustering based algorithm techniques like LEACH,LEACH-C, PEGASIS, etc In WSN sensors are randomly deployed in the sensor field which brings the coverage problem. Hence energy and coverage problem are very scarce resources for such sensor systems and has to be managed wisely in order to extend the life of the sensors and maximizing coverage for the duration of a particular mission. In past a lot of cluster based algorithm and techniques were used. In this paper we also find out all type of PSO based algorithm, their application and limitation over present techniques to overcome the problems of low energy and coverage of sensor range.

Yuanning Liu, Gang Wang,Hao Daong 2011 Particle Swarm Optimization (PSO) is a popular and bionic algorithm based on the social behavior associated with bird flocking for optimization problems. To maintain the diversity of swarms, a few studies of multi-swarm strategy have been reported. However, the competition among swarms, reservation or destruction of a swarm, has not been considered further. In this paper, we formulate four rules by introducing the mechanism for survival of the fittest, which simulates the competition among the swarms. Based on the mechanism, we design a modified Multi-Swarm PSO (MSPSO) to solve discrete problems , which consists of a number of sub-swarms and a multi-swarm scheduler that can monitor and control each sub-swarm using the rules.

Neha Malhotra, IJRIT 108 Dr. Arvinder Kaur and Divya Bhatt 2011 in this research paper, the Particle Swarm Optimization (PSO) technology has been studied and used with the blend of Genetic Algorithm (GA) and the hybrid prioritized algorithm has been proposed. The Particle Swarm Optimization is an optimization algorithm based on heuristic search which can be used to solve time-constraint environment of Test Case Prioritization and the concept of Genetic Algorithm will further help in diversifying the solution within whole search space. For finding the effectiveness of hybrid prioritization algorithm: the efficiency %, saving %, reduction % and APFD/APCC has been calculated.

V.BINARY PARTICLE SWARM OPTIMIZER Model of Binary Decision

The probability that an individual’s of deciding yes or no, true or false, or some other decision depend upon the personal and social factors which are given as

P (xid (t) = 1) = f (xid (t − 1), vid (t − 1), pid, pgd) 1

Therefore deciding of zero is given by (1-P)

P(xid(t)=0)=1−P(xid(t)=1) 2

Where P (xid (t) = 1) is the probability of deciding one at the dth position in bit string.

P (xid (t) = 0) is the probability of deciding zero at the dth position in bit string.

xid (t) is the current state of the bit string site d of individual i.

vid (t − 1) is a measure of the individual’s predisposition or current probability of deciding 1.

t means current time step and t -1 means previous time step.

pid the best state found eg. It is 1 if the individual’s when xid was 1 otherwise 0.

pgd the best state of neighborhood. It is 1 if the best success attained by any member of the neighborhood was 1, otherwise it is zero.

The vid (t) will determine the probability threshold. If its value is high, the individual is more likely to choose one and if its value is low then individual is more likely to choose zero. Therefore such a threshold needs to stay in the range [0.0, 1.0]. So we have sigmoid function to accomplish this which is given as

(vid)=

) v exp(

1 1

− id

+ 3

Therefore, finally formula that is used for decision-making is given as

vid (t) = vid (t-1) + c1

ϕ

ϕ

If ρ_id < s(vid (t))then xid (t) = 1;else xid (t) = 0 4

Neha Malhotra, IJRIT 109 Where ρ_ida vector of random number is lies between 0.0 and 1.0.we should limit vid so that s (vid) does not approach closely to 0.0 or 1.0.A constant parameter Vmax can be set at, the start of a trial to limit the range of vid. Vmax should be set at ±^{4.0 [19].}

VI. ALGORITHM OF PSO Algorithm of PSO is given below:

1: procedure PSO

2: repeat

3: for i = 1 to number of individuals do

4: if G (xr

i) > G (

p r

) then G () evaluates goodness

5: for d = 1 to dimensions do

6: pid = xid. pid is the best state found so far

7: end for

8: end if

9:g=i arbitrary

10: for j = indexes of neighbors do

11: if G (pr_j

) > G (pr_g ) then

12: g = j, g is the index of the best performer in the neighborhood.

13: end if

14: end for

15: for d = 1 to number of dimensions do

16: vid (t) = f (xid (t − 1), vid (t − 1), pid, pgd) update velocity

17: vid∈ ^{(−Vmax, +Vmax)}

18:xid(t)=f(vid(t),xid (t−1)) update position

19: end for

20: end for

21: until stopping criteria

Neha Malhotra, IJRIT 110 22: end procedure

VII. RESULT & DISCUSSIONS

MAGNITUDE

SIGNAL TO NOISE RATIO

IMPULSE RESPONSE

Neha Malhotra, IJRIT 111 PHASE RESPONSE

VIII. CONCLUSION

Designing of FIR filters become more efficient using IPSO. Magnitude response is more linear. Maximum stop band attenuation decreases. Signal To Noise ratio is 20dB. Maximum stop band attenuation is 17.220dB.

Maximum pass band ripple is 0.1570.

IX. FUTURE SCOPE

Incorporating Evolutionary algorithms for multi-modal optimization issues. Making Simulink model of the filter designed by this technique for digital circuits. VHDL simulation & synthesis of the final design for targeting a FPGA or CPLD chip.

X. REFERENCES

[1] L. Litwin, FIR and IIR digital filters, IEEE Potentials.0278- 6648, 2000, 28–31.

[2] T.W. Parks, C.S. Burrus, Digital Filter Design, Wiley, New York, 1987.

Technique Earlier Proposed

Max Stop Band Att 10.97 28.14 Max pass band

ripple

0.1885 .1400

SNR 20.00 48.24

Max stop band ripple

.025 .022

Transition width .094 .092 Execution cycle per

100 cycle

2.9 2.1

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