Filter is a device used to get some desired response. On the basis of the input applied and output produced it is further classified into two types. It is defined by using various terms like range of frequency. Range of frequency is known by a name called bandwidth, which is responsible for the successful communication. Now on the basis of signal processing it is of two types such, as analog filter and digital filter. An analog filter whose input as well as output is analog in nature, whereas the digital filter is defined as the filter having digital input and output. The main concern is about digital filter which is used to improve the quality of the signal so that better signal can be obtained. This is done by removing the harmonic contents from the signal obtained from any digital devices. The digital filter is of two types based on their response. If the impulse response of the filter is infinite, it is called as Infinite Impulse Response (IIR) and when the impulse response of the filter is finite then it is called as Finite Impulse Response (FIR) [2, 13]. IIR is a non linear filter where FIR is a linear filter. The IIR filter is a recursive filter, whereas FIR is a non recursive filter.

The frequency response characteristics of the filter determine the behavior of the filter on the basis of filter parameter used in the design of the filter. Depending on the nature of the signal passing by the filter, it is of four types, i.e. Low pass filter, high pass filter, band reject filter, and band Pass filter. These four categories of the digital filter is a basic filter. The response of these filters is optimized using various techniques like Parks McClellan algorithm, particle Swarm Optimization method (PSO), Harmonics Search Algorithm (HSA), and Opposition based Harmonic Search Algorithm (OHSA), but in all the design techniques some of the drawbacks always exist. These drawbacks are related with ripples present in the pass band, the stop band attenuation, and the transition width. Tizhoosh in his work gives the idea of Opposition-Based Learning (OBL) [19,20] to obtained filter with optimized results. The optimization is meant to improve the certain parameters present which are required in the design of the filter. This optimization includes reduction of ripples in the pass band, reduction of transition width because as small as the transition width between pass band and stop band, the design will be near about ideality. Based on the types of systems it is of two types. When the system performs filtering operation in time domain then it is digital filter and when filtering is done in frequency domain, it is spectrum analyzer. In the design of filter in digital signal processing, the digital filter plays a very important role. From both the filters, i.e. FIR and IIR, the advantages of FIR over IIR are due to its linear nature because linearity properties of any devices are a very important property. These advantages of FIR over IIR are as follows: linear phase, linear design method, and always stable [12].

The main aim of this paper is to compare the two algorithms, viz., Harmony Search Algorithm and Opposition based Harmony Search Algorithm. So the optimized FIR filter can be designed. The convergence rate and ripples in the passband are the main factors which are compared in this paper.

Shukla and Mishra (2014) proposed a new method Dynamic and Adjustable Particle Swarm Optimization (DAPSO) and Particle Swarm Optimization with Variable Acceleration Factor (PSO-VAF) in Linear Phase Digital Low Pass FIR Filter to reduce the problem of ripples in pass band and stop band, also this method is capable of controlling ripples in both the bands [16].

Singh et al. (2014), proposed the Particle Swarm Optimization using constriction factor approach for nonlinear, non-differential, multi-modal LP FIR filter design problem. This methodology has best convergence characteristics with very small number of iterations and eliminates the problem of non-linear, non-differential, multi-modal LP FIR filter design [17]. The proposed method to find the best solution of FIR filter design problem is Cuckoo search algorithm [18].

Zhang et al. (2014), in their work, evolutionary technique has been obtained end in one step, due to this, the exploration and exploitation within the evolution method becomes unbalance. The projected algorithm has a twostage penalty which is applied to the unfeasible solutions. In the initial stage, the algorithm will search for possible solutions with better objective values with efficiency. In the second stage, the algorithm will take full advantage of the knowledge contained in unfeasible individuals and avoid trapping in native (local) optimum. Additionally, for adapting to the present technique, a New Harmony search algorithm is conferred, which can keep a balance between exploration and exploitation in the evolution method [24].

Wang et al. (2014), explained that, in original harmony search algorithm, global improvement problem exist. The projected technique is completely different from the first Harmony Search (HS) in three aspects. Firstly, opposition based learning method is incorporated to the method of improvisation to increase the algorithm search space. Then, a new hybrid mutation strategy is designed rather than the first pitch adjustment process of Harmony Search to further improve the searching ability of HS. Effective selfadaptive strategy is conferred to fine-tune the key control parameters (e.g. Harmony Memory Consideration Rate (HMCR), and Pitch Adjustment Rule (PAR)) to balance the local and global search within the evolution of the search method [22].

Gonsalves and Egashira (2013), examined that, since the FIR response depends on various parameters, the convergence rate is not better, so to achieve the better convergence rate, additional parameters are required to introduce in the original PSO. But this additional parameter destroys the simplicity of the algorithm and leads to an undesirable computational overhead [5]. Ammar et al. (2013), explained that better convergence speed into the global optimum can be achieved by using two hybrid optimization methods based on Harmony Search algorithm (HS) and two different nature inspired metaheuristic algorithms. The basic idea of hybridization was to ameliorate all the harmony memory vectors by adapting the PSO velocity or the DE operators in order to increase the convergence speed [1].

Ghoshal et al. (2013) proposed a work to obtain the ideal frequency response characteristics of all the FIR filters, using a new meta-heuristic search method, called firefly algorithm. Firefly Algorithm was inspired by the flash pattern and characteristics of fireflies [14].

Saha et al. (2013), demonstrated that, the planned technique HS performs a structured irregular search of an unknown vector inside a multidimensional search space for locating the best resolution. Better exploration and exploitation of entire search space makes sure the rejection of premature convergence and stagnation issues that are more or less typically present with standard RGA, PSO and DE [15].

Cui et al. (2013) adopted the mutation and crossover operations instead of harmony memory consideration and pitch adjustment operation, which very much improves the convergence rate. Furthermore, the key parameters like mutagenic factor and crossover rate are adjusted dynamically to balance the local and global search [3].

Gao et al. (2012), according to them, since various evolutionary methods suffer sometimes from slow search speed and fails to find the global optima in an efficient way. The proposed work uses the hybrid optimization approach, into which the Harmony Search is merged together with the Opposition-Based Learning (OBL) [4]. Vural et al. (2012), evolved that classical evolutionary algorithm suffers from approximation error during a short computation time. The planned Hybrid algorithm are quick and economical evolutionary algorithms, Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), Differential Evolution (DE), Harmony Search (HS) are used to optimize the divisor coefficients of the low-pass filter transfer function [21].

Jing et al. (2012), explained that the performance and convergence rate of the method are suffered when handling high-dimensional or/and multimodal issues. The hybrid HS rule is proposed to induce a far better control between exploitation and exploration. This is often characterized in two aspects. First, the memory thought theme is changed by introducing crossover and mutation operators that is inspired by the Differential Evolution (DE) rule. Second, two control parameters, particularly PAR and BW, are either dynamically adjusted or self-learning together with the evolution method to fine-tune the solutions [6].

Yang and Zhu (2012), introduced modified harmony search algorithm to improve the performance of its algorithm, which will balance the diversification and intensification on the basis of global harmony search algorithm [23].

Changming and Lin (2011) proposed a new improved harmony search algorithm based on the current global information (IGHS) for solving continuous optimization problems. In order to avoid premature and enhance global search ability, this method disturbs the current global optimum at a certain probability [8].

Mandal et al. (2011), in the design process, the filter length, pass band frequencies and stop band frequencies, the feasible pass band and stop band ripple sizes are mentioned. FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. The Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSO-CFIWA) algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristic [10].

Prasad et al. (2011), designed FIR band stop filter using Craziness based Particle Swarm Optimization (CRPSO) approach to generate a set of optimal filter coefficients and tried to meet the ideal frequency response characteristics for different orders of the filter [9].

Mukherjee et al. (2011), scrutinized that the multi-modal optimization problems of the FIR filter and the conventional gradient based optimization techniques are not efficient for digital filter design. The proposed method, IPSO is an improved PSO that proposes a new definition for the velocity vector and swarm updating and hence the solution quality is improved [11]. Hong and Li (2007), indicated that, from original particle swarm improvement technique, high dimensional improvement isn't possible, therefore the projected hybrid technique (NHPSO) is proposed so as to solve high dimensional improvement issues additional with efficiency, accurately, and faithfully. It provides a new design of hybrid algorithms that organically merges the Harmony Search (HS) technique into Particle Swarm Improvement (PSO). During the course of evolvement, harmony search is employed to enhance the search performance and this makes NHPSO algorithm have more powerful exploitation capabilities [7].

From the literature review, the authors have found a number of problems associated with the design of linear phase FIR filter design, such as convergence rate, nonlinear, non-differential and multi-modal, deterioration in the transition width, etc. There is also difficulty in the design of the filter with minimum ripples in pass band and stop band.

To design a better filter, an additional parameter destroys the simplicity of the algorithm and leads to an undesirable computational overhead [5]. Firefly Algorithm was inspired by the flash pattern and characteristics of fireflies, but this algorithm is little bit complex in nature, due to its irregular search nature [14]. The balancing of local and dynamic search is quiet tough in this algorithm. This is done by adjusting mutagenic factor and crossover rate, which make this algorithm complex [3]. Estimates and counterestimates, weights and opposite weights, and actions versus counter-actions are the main problems considered [19]. Slow search speed and fails to find the global optima in an efficient way is the major problem of Harmony search algorithm [4]. The problem of ripples in pass band and stop band and to control ripples in both the bands were considered [16]. The problem of non-linear, nondifferential, multi-modal LP FIR filter design were considered [17]. Evolution method considered the problem of balance between exploration and exploitation [24]. The classical evolutionary algorithm suffers from approximation error during a short computation time [21]. The performance and the convergence rate of the method are suffered when handling high-dimensional or/and multimodal issues [6]. In order to avoid premature and enhance global search ability, this method disturbs the current global optimum at a certain probability [8]. An original particle swarm is having the problem of high dimensional improvement [17]. FIR filter design is a multimodal optimization problem. The conventional optimization techniques are not efficient for digital filter design [18]. The approximating function does not satisfy the Haar condition, the optimal solution is not necessarily unique, and a straightforward extension of the onedimensional exchange method may fail to converge [13].

From this work, it can be concluded that the Opposition based Harmony Search Algorithm is better than Harmony Search Algorithm. From the study of many works, we have seen various problems such as convergence rate which are not better, due to which the filter response are deteriorated at some extent. Evolutionary methods suffer sometimes from slow search speed and fail to find the global optima in an efficient way. To achieve the better convergence rate in any of the previous methods, some additional parameters are used which destroys the simplicity of the algorithm and leads to an undesirable computational overhead. The problem of non-linear, nondifferential, and multi-modal are in the designing of FIR filter. The problems of premature convergence and stagnation are more or less usually present with conventional RGA, PSO, and DE. The exploration and exploitation of the search space in the evolution process becomes unbalance due to this search for feasible solutions with better objective values would be inefficient. The classical evolutionary algorithm suffers from approximation error in a short computation time. Sometimes magnitude response, minimum stop band ripple, and maximum stop band attenuation are obtained, but with a very little deterioration in the transition width. The problem of the FIR filters with the ability to converge to the best quality near optimal solution and possesses the best convergence characteristics. Difficult to design filter with minimum ripples in pass band and stop band and many of the filters design method were unable to control the ripples in both bands separately. To achieve better response of the optimized response, various methods have been designed which were able to remove various problems, but none of the methods can achieve better response in removing all the problems associated with the optimization of filters. From all the problems, we have considered only two problems for comparison, i.e. convergence rate and the ripple in the passband.

I would like to acknowledge my gratitude to a number of people who have helped me in different ways for the successful completion of my thesis. I take this opportunity to express a deep sense of gratitude towards my guide, Mr. Dharmendra, Assistant Professor (ET&T), SSIPMT, Raipur for providing excellent guidance, encouragement and inspiration throughout the project work. Without his invaluable guidance, this work would never have been a successful one. I am thankful to Mrs. Hemlata Sinha, HOD, ET&T Department, and Dr. M.L. Dewangan, Director, SSIPMT, for their kind help and cooperation. I would also like to thank all who helped us in doing our work for their kind support and helpful suggestions. I feel immensely moved in expressing my indebtedness to my parents whose sacrifice, guidance and blessings helped me to complete my work.