A Novel Framework for FIR Digital Filter Design Based on P system with PSO

Digital filter plays an important role in the digital signal processing, with a wide range of theoretical and practical application. The essential characteristic of the digital filter is that it can make the useful signal as much as possible all go through, while maximally suppress the useless signal. Due to the structure and function of digital filter, the classical filter design methods will suffer from some shortcomings: slow convergence and local minimums. To overcome the shortcomings in FIR filter design, a novel P systems-based method for optimal FIR filter design under the framework of P system is proposed by combining parallel property of P system, which is named as Tissue P Systems algorithm (TPS). In the proposed TPS model, instead of traditional design methods, a star tissue P system is designed as its computing framework, while the impulse response coefficients of the filter are regarded as the objects in the elementary membranes. Each object in cells expresses a group of filter coefficients to be optimized by using velocity-position model of PSO, and inherent communication mechanism is used to share the objects among different elementary membranes, so as to determine the optimal filter parameters. Low-pass filter (LP), high-pass filter (HP), band-pass filter (BP) and band-stop filter (BS) are employed to verify the effectiveness of the proposed method. Five state-of-the-art design methods, which are Parks-McClellan (PM), real-coded GA (RGA), particle swarm optimization (PSO), differential evolution (DE) and opposition-based harmony search (OHS) are used to exhibit the advantages of the proposed framework. The comparison results demonstrate the proposed TPS model that obtains better performance regarding magnitude response, with minimum stopband ripple, and maximum stopband attenuation. Moreover, the simulation results also show that the proposed FIR filter can close the requirements of ideal filter to the maximum extent.