Abstract
This chapter presents a mutation-based particle swarm optimization (PSO) approach for designing a linear phase digital low pass FIR filter (LPF). Since conventional gradient-based methods are susceptible to being trapped in local optima, the stochastic search methods have proven to be effective in a multi-dimensional non-linear environment. In this chapter, LPF with 20 coefficients has been designed. Since filter design is a multidimensional optimization problem, the concept of mutation helps in maintaining diversity in the swarm population and thereby efficiently controlling the local search and convergence to the global optimum solution. Given the filter specifications to be realized, the Mutation PSO (MPSO) tries to meet the ideal frequency response characteristics by generating an optimal set of filter coefficients. The simulation results have been compared with basic PSO and state of artworks on filter design. The results justify that the proposed technique outperforms not only in convergence speed but also in the quality of the solution obtained.
TopBackground
Optimum FIR digital filter design using computational intelligence based optimization algorithm is described in (Teixeira & Romariz, 2007) (Flavio, 2007). A comparison of the Genetic Algorithm (GA) and PSO techniques for the design of the FIR filter are described in works by (Najjarzadeh & Ayatollahi, 2008)(Ababneh & Bataineh, 2008). The authors have indicated PSO to be a better performer. Differential evolution PSO(DEPSO) for the design of digital FIR filter design is described in (Luitel & Venayagamoorthy, 2008)(Reddy & Sahoo, 2015). PSO with constriction and time-varying inertia weight for the design of the high pass filter is described in (Kar, Mandal, & Ghoshal, 2011). Improved PSO for the design of the high pass filter is proposed in (Mandal et al., 2012). The Artificial Bee Colony algorithm has been used for the design of a low pass filter by Dan Ji(Ji, 2016). A comparative study of Cuckoo search (CS), PSO and ABC optimization methods for linear phase FIR filter design is also presented in the works by (Sharma, Kuldeep, Kumar, & Singh, 2016). PSO algorithm based on refractive opposite learning has been proposed for the design of FIR low and high pass filters(Shao, Wu, Zhou, & Tran, 2017). Recently, the Whale optimization algorithm has also been proposed for the low pass filter design (Mukherjee, Chakraborty, & Das, 2017).
Key Terms in this Chapter
Multidimensional Optimization: It refers to finding the maximum or minimum of a function in many variables.
Optimization: It is a scientific discipline that deals with the detection of the optimal solutions among the alternatives.
Particle Swarm Optimization (PSO): It is an optimization technique based on the social and the cooperative behavior of bird flocking.
Mutation in PSO: It refers to some random tweak in the particle position to get a new solution.
Premature Convergence: It refers to a condition in which the population for an optimization problem converged too early, resulting in a suboptimal solution or fitness value.
Evolutionary Computation: It refers to the collection of problem-solving approaches that are based on concept of biological evolution.