IIR Filter Design Using African Buffalo Optimization

In the modern world, the digital signal processing embeds more in real time applications. Several researchers focused on filtering process to identify the limitation in traditional methods. In this article, the meta-heuristic algorithm is deployed for optimizing infinite impulse response (IIR) filter design. The traditional IIR filter results create computational complexity and its performance is worse in the case of a noisy environment. In signal processing, IIR plays several roles in filtering and monitoring the signal amplitude. The African Buffalo Optimization (ABO) is quite easy for implementation and its performance outcomes solved many problems in various domains. Hence, it is selected for solving IIR filter problems for obtaining optimal filter coefficients. Initially, IIR filter is designed for different orders under ABO concept. The ABO based IIR filter’s performance is superior to those obtained by Genetic Algorithm and cuckoo search algorithm. The proposed method’s performance result proves that it has a smaller magnitude error and phase error with fast convergence rate.


Introduction
Most of the filtering applications are used for reducing or eliminating the noise and allows required original message signal. While entering into the specific application area, the filter is classified into the analogue and digital filter. The digital filters are mostly used for calculation purpose. Some windowing techniques are used traditionally to solve complex filtering process. The windowing technique's drawback is, it doesn't have any sufficient control in varying frequency bands.
In recent days, a digital filter actively plays a major role in real time applications like image processing, video processing and in some medical processing. Traditionally, the filter design is carried out with the help of several domains, namely, Digital signals Processing, Very Large-Scale Integration, etc., The filter design is separated into two major fields, termed as recursive and non-recursive. The recursive filter's examples are Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) is Non recursive. In these two cases, the most commonly used method is the IIR filter because it may supply better performance than FIR filter with similar coefficients.
In IIR filter applications, the reliability is missing due to the multi-modal error surface problem. Hence, it is important to design a reliable model based on global search optimization. Traditionally, researchers [1] focussed on global optimization techniques known as Particle Swarm Optimization in filtering appliances and more. In such cases, the filtering process is managed by different fitness functions and mean square error response. Therefore, an Evolution Particle Swarm Optimization (DEPSO) is also one of the best procedures for designing for dynamic filter environment.
Previously, [2] presented neural network-based filter to minimize the weighted square-error. Similarly, [3] presented a finite word length filter according to Particle Swarm Optimization as well as Genetic Algorithm (GA). [4] presented an extension of the normal filter which is carried out using Artificial Bee Colony (ABC) algorithm. The objective of this work is to enable the filter structure and operation with an efficient phase response and coefficient quantization error with a globally optimal solution. In this paper, inspirations from the behaviour of African buffalos are applied for digital filters design. African Buffalo Optimization has been used here for the design of linear phase FIR filters. The designed method is compared with the normalized frequency and magnitude to show the effectiveness of the design. As shown in Figure 1, the system identification process is carried out by varying the IIR filter with African Buffalo optimization technique. Many researchers focused on evolution algorithm to deal with the exact functions. Hence, in this research, the parameters are arranged by the ABO process until elimination or minimization of unwanted noise present in between the unknown and known output.
The remaining part of this work is organized as follows. In section 2, the recent reviews are handled based on the traditional filtering process and global search optimization-based filtering process to find the exact limitations. The detected limitations are defined as a problem and mentioned in section 3. The total design optimization is carried out with the help of an African Buffalo algorithm in section 4. The corresponding experimental evaluation is carried out in section 5. Finally, the article is concluded with its merits and some future extension at section 6.

Literature Survey
The survey describes the different types of filtering concepts based on architecture, low power applications, evolutionary applications and so on. To verify the exact way of implementation and find the optimal solution, it is important to review the related concepts.

FIR Filter Design based on architecture
In real time applications, there is a need for reconfigurability. The process is framed with a reconfigurable substrate with the help of several multipliers fewer filter options. In memory operations, the filtering options are required to manage the complete process. In such cases, the process is converted into the several combinations of adder and multiplier. The multiplier is one of the important factors managed by the repeated addition process. Hence, the major objectives handled in that unit are to reduce the adder unit to reduce the complexity. If a single internal delay is reduced, then the overall delay is reduced with the help architecture.
[5] presented a FIR filter with high throughput. It is used here to improve the speed. The major limitations of traditional FIR filter processing are delayed because based on the word length the delay will be added and frame lot of corrections. Hence, the pipelining concept is added to improve the speed by reducing the delay. Apart from the speed, power delay and latency is also considered or evaluating the Filter design. Another form of reducing the complexity is Factorial Canonical Signed Digit (FCSD) based design is framed to replace the multiplication unit with the shift and addition units. The process helps to identify the merits with the help of Lookup table. It is designed under MATLAB and Xilinx by [6].
[7] presented a hybrid model with Genetic Algorithm (GA) and the Taguchi method. Taguchi process is successfully implemented in between the crossover and mutation process. The process is tested under different filterings like low-pass (LP), band pass (BP), high-pass (HP) and band stop (BS). [8] presented a filter design using Distributed arithmetic transformations. The main advantage of choosing this architecture is minimum processing time and fewer registers. The parallel operation of this algorithm is considered as the reconfigurable units. The large block sets are processed to reduce the delay. The important aspects of designing the filter are increasing the speed even if the block sets are increased. By increasing the filter length, the block size is also getting increased. [9] have discussed an adaptive Infinite-Impulse-Response (IIR) filter structure with particle swarm optimization. It is designed with desired filter output, which is corrupted by noise. It helps to provide a simple implementation that has an ability to provide a good solution. The existing filter designs have limitations of low accuracy and minimum convergence rate. Further, the work is extended for tuning the filter into required accuracy.
As shown in Table 1, the survey discussed the IIR filter concept based on different architectural types. Its performance is considered based on the low power consumption, efficiency, and accuracy. To verify the functionality, the implementation is also considered for review. Filter in Low Power Implementations [10] presented an application based Defected Ground Structure (DGS) in low-pass filters. [11] proposed a new, effective algorithm to reduce finite-impulse response complexity via resource sharing. Initially, rounded Canonical Signed Digit (CSD) coefficients are considered here for managing all coefficient set. Here, quantization error's magnitude is managed with local search method.
The FIR synthesis provides a better solution.
To obtain the lowest power concepts some traditional methods are assumed for designing the FIR filter. Based on the input signals the filtering units are processed. In a dynamic environment, the processing field varies with the stopband energy. Hence, to achieve low power in filtering the author [12] proposed an algorithm for approximate processing concepts. It is verified in the field of lowpass filtering applications and parallely applied to several other applications.
Although traditional methods PSOIIR, CSO shows a good performance to find promising solution for different problems. But still, it is inefficient to determine global optimum with respect to convergence speed and quality. Hence, there is a necessity to develop the optimized algorithmic concept for filtering applications.

Research Methodology
Under this section, the traditional evolution algorithms namely Genetic Algorithm and Cuckoo Search Optimization are discussed to find the exact problem.

Genetic Algorithm
Genetic algorithms based on the principle of the survival of the fittest are evolutionary statistical models of natural selection. With each new generation, the differences are added into a population, the less-fit individuals begin to die off in the food race, and this survival of the fittest theory contributes to species changes. The principle of natural selection has been used to understand how animals have been able to adapt to evolving habitats, so organisms that are somewhat similar in adaptability may have evolved.
This scheme's usual function is to have the exact solution to the unique problem. Each entity in the population similar to chromosomes in natural systems is called a string or chromosome. The population size defines the amount of information stored by the GA. The population is noticed on the basis of generation. The chromosome is one of the important aspects of creating the appearance and behavioural feature of each organism. The disadvantages of genetic algorithms and all other heuristic algorithms are the loss of optimality but in practice, it has been shown that the results are often of high quality. To solve the problem in a genetic algorithm proposed method of cuckoo search optimization is introduced.

Cuckoo Search Optimization
The new Meta heuristic algorithm, inspired by evolution, is a Cuckoo Search Optimization algorithm. The algorithm is based on the breeding behaviour of some types of cuckoos, such as brood parasitism. By extracting the eggs of host birds, cuckoos lay their eggs in communal nests, thus increasing the hatching chance of their own eggs.
There is no chance of recalling the previously visited answers in the simple version of the cuckoo search algorithm. The algorithm starts with a group of solutions that are filled with a series of nests that are randomly generated. In each nest, the number of eggs is set and equal. It is considered that the number of cuckoos is proportional to the number of nests. Eggs represent a possible solution here. In the proposed algorithm, too the principles of the simple Cuckoo search algorithm are implemented. The theories are 1) One egg at a time is laid by each Cuckoo and dumped in a randomly selected nest.
2) The next generation brings the best nest of highquality chicks.
3) The number of host nests available is fixed. The content of eggs is proportional to the objective function's fitness value. In each nest, the best egg and hence the latest best solutions are discovered and registered accordingly. The latest solution is every Cuckoo's egg. This latest egg is a substitute for the worst egg in the picked nest.
Cuckoo Quest (CS) is an optimization algorithm that was generated in 2009 by [13] describe an outline of CS inspired by the life of a bird family called Cuckoo, as well as an overview of CS applications to solve optimization problems in different categories. The purpose of this paper is to provide an outline and to summarise the analysis of the CS implementation. [14] suggested the Cuckoo Search Clustering Algorithm based on levy travel (2013). This algorithm is the implementation of the Cuckoo Search Optimization algorithm to locate the cluster's optimal centroids and to find the clustering algorithm's global solution in a web document clustering area. [15] introduced a new algorithm for metaheuristic optimization, dubbed cuckoo search, to solve structural optimization tasks. In combination with Lévy flights, the latest CS algorithm is first tested using a nonlinear benchmark constrained optimization problem [16]. For the most part, the optimum solutions obtained by CS are much better than the optimal solutions obtained by the current methods [17].

Proposed Filter Design
The African Buffalo Optimization is one of swarmintelligence techniques used to solve various continuous problems with respect to the benchmarks. It is evolved from the animal's instincts and search techniques that utilize in the American forests and savannahs. It is an intelligent, cooperative and democratic attitude in its search for the optimal path. The module is designed by considering the IIR filter Input-output relation. The input x(k) and its output y(k) depend on filter order M. The filter coefficient ai, bi considered to determine overall filter characterize. Hence, filter coefficients are processed by the optimization algorithm.

Fig. 2: Flow chart for proposed ABO process
The metaheuristic algorithm employs a global search mechanism and local search mechanism, it has several advantages when compared with many other algorithms such as Genetic Algorithm (GA), Particle swarm optimization (PSO) algorithm, Bee Colony Optimization (BCO) and so on. The decision making and search, candidates are best in this type of algorithm. Several key features of a good algorithm are, it has an ability to identify the best solution in real time streaming or iteration. The survival of the fittest solution is one of the best ways to represent the current best found as discussed by [18]. Hence, by several factors, the African buffalo optimization is attempted for complementing existing algorithms for solving problems of delay and inefficiency [19].
Step1. Objective function f(x) x= (x1, x 2 , ……… x n ) T Step2. Initialization: randomly place buffalos to nodes at solution space; Step3. Update buffalos fitness values by following equation W.k+1 = w. k + lpr 1 (bg maxt.k -m. k ) + lpr 2 (bp max.km. k ) Where w. k and m. k represents exploration and exploitation moves respectively of k th buffalo (k= 1, 2…N); lp1and lp 2 are learning factors; r 1 and r 2 are random numbers between [0, 1]; bgmax is the herd's best fitness and bp max, the individual buffalo's best Step4. Update buffalo k's location in relation to bp max.k and bg max.k using m. k +1 = λ (w. k + m. k ). Where 'λ' is a unit of time Step5. Check bg max is updating or not. If yes, go to 6. else, go to 2 Step6. If stopping criteria is not met, go back to algorithm step 3 Step7. Output best solution.
As shown in the Figure 2, the first step of ABO comprises of randomly considering a set of the population (buffalos) and performing crossover and mutation on that population to produce the solutions. The crossover rate and the mutation rate is considered after these operations, the ABO produces set of buffalos location and tested it in channel allocation process.

Simulation Results
In this section, Genetic algorithm's performance is compared with that of a traditional PSO algorithm. Then the problem is identified to manage the test functions with African Buffalo optimization. Finally, the GA, PSO and ABO algorithms are applied to design a digital IIR filter. A traditional form of GA is considered to perform IIR digital filter design. In such cases, the process is implemented by selection, crossover, and mutation.  Figure 3, IIR LP filter is designed by ABO shows that pole-zero plot contains all poles lies in a unit circle which shows system is stable. The frequency response plot is represented in Figure 4. From the analysis, it is concluded that, the attenuation is reduced and its efficiency is improved indirectly.

Conclusion
For designing a digital low-pass IIR filter, African Buffalo Optimization (ABO) technique is proposed in this paper. Major advantages of proposed ABO technique include easy implementation, robustness and controllable convergence speed. In top-band and pass band, least ripple magnitude and magnitude error are produced by the proposed ABO as realized in the results. In MATLAB, experimentation was performed and it indicates the robustness and stability of the system. The proposed ABO technique is highly powerful and effective in digital IIR filter design. In any filter types like BS, BP, HP and LP, proposed ABO can be applied as concluded. From the result, it can be determined that proposed ABO method is superior to traditional GA and PSO. In future, extend this algorithm for real time design optimization problem.