Low delay digital IIR filter design using metaheuristic algorithms

Digital IIR filter design by optimizing a fitness function with respect to coefficients of a filter with rational transfer function by meta-heuristic algorithms has been considered recently. Most researchers use a fitness function consisted of difference between magnitude response of desired filter and designed filter and the constraints such as linear phase, minimum phase and stability of designed filter. In this paper, a comprehensive fitness function for IIR digital filter design with 6 terms is proposed. A new term is added to fitness function to get a filter with low delay. Low delay filters are desirable for real time signal processing. This term is weighted partial energy of the impulse response of designed causal filter. Maximizing this term leads to concentration of energy of impulse response at its beginning, consequently a low delay filter. Low delay property leads to fast decaying of transient response and low delay between input and output of designed filter. Proposed fitness function also includes some terms to meet linear phase, minimum phase and stability constraints. Meta-heuristic optimization algorithms GA, GSA and PSO are used to optimize proposed fitness function. To evaluate efficiency of the proposed method, it will be used to design a low delay low pass filter and a low delay differentiator. Reported results show lower delay of designed filters by proposed method than designed ones by traditional methods.