基于遗传算法和余弦序列的数字滤波器设计

FIR Digital Filter Design Based on Genetic Algorithm and Cosine Sequences

有限长单位脉冲响应(FIR)数字滤波器具有系统稳定、线性相位、实现简单等优点,在数字信号处理领域得到了广泛应用;遗传算法具有记忆性、分布性和多样性等优点,广泛用于智能计算、模式识别、优化设计等领域。本文提出了基于遗传算法和余弦序列相结合的FIR数字滤波器设计方法,即采用对余弦序列加权求和方式生成窗口函数,而加权系数通过遗传算法求解得到,并采用加窗方法实现数字滤波器。为了提高收敛速度和收敛精度,采用了精华模型和浮点编码等有效手段。以低通数字滤波器为例进行了仿真实验,实验结果验证了设计算法的有效性。本文提出的数字滤波器设计算法具有设计灵活、适应广泛、容易实现等优点。

Digital filter with Finite Impulse Response(FIR) has lots of advantages,such as systemic stability,linear phase,etc. It has been widely used in digital signal processing. The genetic algorithm has lots of merits,such as the memorability,distribution,and diversity. It is widespread in the fields of intelligent computation,pattern recognition and optimization design. This paper presents a designing method of digital filter. It is based on the combination genetic algorithm with the cosine sequences. The window function is constructed effectively by weighting cosine sequences. The corresponding weighting coefficients are computed by the genetic algorithm. Digital filter is realized finally by windowing approach. In order to accelerate the convergent speed and improve the precision,elitist model and floating-point coding are adopted. The efficiency of the proposed method is validated by simulation experiments taking on designing low pass digital filters. The designing method presented in this paper has some advantages,such as good flexibility,universality,and so on.