Fractional Order Filter Discretization by Particle Swarm Optimization Method
Fractional-order filter functions are generalization of rational filter functions, which includes integer order filter functions. Fractional-order filters present advantages of more options in frequency selectivity properties of filters compared to integer order counterparts. This study presents an application of Particle Swarm Optimization (PSO) for IIR filter discretization of fractional-order continuous filter functions. The proposed method enforces particles to search in stable filter search regions and ensures the stability of optimized IIR filter functions that approximate to amplitude response of continues fractional-order filter functions. In this chapter, illustrative filter discretization examples are demonstrated to show results of PSO algorithm and these results are compared with results of Continued Fraction Expansion (CFE) approximation method. Stop band approximation performance is very substantial for band reject filter design. We observed that proposed discretization method can provide better approximation to the amplitude response of fractional-order filter functions at the stop bands compared to CFE approximation method.
KeywordsFractional order filter Discretization Particle swarm optimization method Continued fraction expansion Nyquist sampling theory Tustin discretization Objective function Optimization Phase response approximation
This study is based upon works from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).
- 1.Ates, A., Kavuran, G., Alagoz, B.B., Yeroglu, C.: Improvement of IIR filter discretization for fractional order filter by discrete stochastic optimization. In: 39th International Conference on Telecommunications and Signal Processing, 2016, Vienna (2016)Google Scholar
- 4.Das, S., Majumder, B., Pakhira, A., Pan, I., Gupta, A.: Optimizing continued fraction expansion based IIR realization of fractional order differ-integrators with genetic algorithm. In: 2011 International Conference on Process Automation, Control and Computing (PACC). IEEE, Coimbatore (2011)Google Scholar
- 15.Saha, S.K., Kar, R., Mandal, D., Ghoshal, S.P.: Optimal IIR filter design using novel particle swarm optimization technique. 2012. Int. J. Circuits Syst. Signal Process. 6(2), 151–162 (2012)Google Scholar
- 16.Heris, M.K.: Particle Swarm Optimization in Matlab. http://yarpiz.com/ (2017). Accessed in Feb 2017