基于改进遗传算法的滤波器优化设计
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摘要
采用遗传算法的思想用于滤波器优化设计是近年来设计滤波器的研究热点之一。本文主要研究采用改进的遗传算法进行有源滤波器的优化设计以及头部相关传递函数(HRTFs)的逼近问题。
论文首先阐述了遗传算法的基本概念、构成要素、特点及遗传算法的改进技术,接着介绍了滤波器的基本原理、基本构成及经典设计方法,然后从改进的遗传算法对滤波器的优化设计方面展开一些探索性的研究。本文的主要贡献如下:
1.深入研究了滤波器的设计理论。有源滤波器具有体积小、便于集成等优点,得到了广泛应用,对有源滤波器设计方法的改进有非常重要的意义。遗传算法(GA)是模拟生物在自然环境中的遗传和进化过程而形成的一种概率搜索算法;而全局优化的优化方法是从总的传递函数出发,对电路参数进行设计。本文将遗传算法和全局优化的思想融合到一起来逼近切比雪夫有源低通滤波器。实验结果表明,这种方法克服了传统方法的一些不足之处,逼近效果有明显的改善。
2.本文提出了改进的遗传算法逼近HRTFs。针对传统遗传算法逼近效果误差较大的问题,结合空间听觉的研究成果,从染色体编码、种群的初始化、适应度函数的设计,到遗传操作操作数的设计、染色体解码等具体问题都提出了新的解决方案,如采用改进的选择方式、提出自适应遗传算法、提出精英选择策略以及提出最优引导策略。在遗传算法运行的后期阶段,对个体的适应度进行适当的放大,扩大最佳个体适应度与其他个体适应度之间的差异程度,以提高个体之间的竞争性。从实验结果可以看出改进的遗传算法的逼近效果明显优于传统的遗传算法及Prony算法。
3.耦合器是一种应用十分广泛的微波电路,它可以用于组成滤波器,例如双光纤定向耦合器组成光学梳状滤波器;在滤波器滤波以后为了把信号进行分路传输要用定向耦合器,定向耦合器是多端口的器件。本文将遗传算法用于多级分支定向耦合器的优化设计并对算法进行了改进。设计中取消了主线、分支阻抗左右对称的限制,使设计的自由度进一步加大,主、副线的特性阻抗采用优化设计方法确定,分支定向耦合器的工作带宽得到了进一步扩展;在标准遗传算法的基础上,引入了最优保存策略和自适应遗传操作,算法的性能得到了提高。仿真表明,用该方法设计的多级分支定向耦合器性能优于其他设计方法。
论文最后总结了本文的工作,并提出进一步的研究探索方向。
It has been a hot research spot to adopt genetic algorithms (GA) for optimal filter design recently. The primary research of this paper concentrates mainly on the optimization design of active filters with improved genetic algorithm and the approximation problem of head-related transfer function (HRTFs).
The thesis first expounds the related theory of genetic algorithms, such as the basic concept, components, characteristics and the improved technology of genetic algorithms. Second, it carries out some exploring research in the aspect of genetic algorithm’s optimal design on filters. The major contributions made by the research are as follows:
1. Further research into the design theory of filter. Active filters is widely applied for its advantages, such as small volume and easy integration, thus showing great significance to the improvement method of the active filters. Genetic algorithm is a probability search algorithm formed by simulating life's descendiblity and evolution process in nature; Global optimization method of the circuit parameter design, which is based on total transfer function, carries out design of circuit parameters. This thesis combines genetic algorithm and the idea of global optimization together to design the Chebyshev low pass. The results show that this idea overcomes some shortcomings of traditional methods and has obvious improvement.
2. This thesis puts forward the idea that the improved genetic algorithm approximates HRTFs. To solve the problem that there is a big error caused by the traditional genetic algorithm, this research makes use of the outcomes of space hearing and provides new solutions to chromosome coding, population initialization, the designing of fitness function and genetic operations, and decoding chromosome as well. Examples are adopting improved ways of choosing, putting forward adaptive genetic algorithm, elite selection strategy and best guide strategy. In the late period of the function of genetic algorithm, properly enlarging the degree of fitness of individuals, broadening difference between the best individual fitness and that of other individuals serve to increase the competition among individuals. As is revealed from the results of the experiment, the approximation of improved genetic algorithm is obviously better than that of the traditional algorithm or Prony.
3. Coupler is a kind of microwave circuit applied widely, which can compose filter , such as dual directional coupler can compose optical comb filter.After filtering, for the signal broadband transmission, we should use the directional coupler, which is the multi-port device. This paper uses genetic algorithm in optimum design of the multiple grade branch directional coupler and makes some improvements in algorithms. The design abandons the limit of balance between the main line and branches, which leads to strengthening the freedom of design work. The optimum design method determines the characteristic impedance of both main lines and braches, as a result of which the bandwidth of the directional coupler is broadened. Based on the standard genetic algorithm, the best storage strategy and fitness genetic operations are brought in to improve the performance of the algorithm. Simulation shows that multiple grade branch directional coupler designed with this method performs better than any other design method.
The thesis finally makes conclusions about the research that has been done and puts forward as well the direction for further research.
论文首先阐述了遗传算法的基本概念、构成要素、特点及遗传算法的改进技术,接着介绍了滤波器的基本原理、基本构成及经典设计方法,然后从改进的遗传算法对滤波器的优化设计方面展开一些探索性的研究。本文的主要贡献如下:
1.深入研究了滤波器的设计理论。有源滤波器具有体积小、便于集成等优点,得到了广泛应用,对有源滤波器设计方法的改进有非常重要的意义。遗传算法(GA)是模拟生物在自然环境中的遗传和进化过程而形成的一种概率搜索算法;而全局优化的优化方法是从总的传递函数出发,对电路参数进行设计。本文将遗传算法和全局优化的思想融合到一起来逼近切比雪夫有源低通滤波器。实验结果表明,这种方法克服了传统方法的一些不足之处,逼近效果有明显的改善。
2.本文提出了改进的遗传算法逼近HRTFs。针对传统遗传算法逼近效果误差较大的问题,结合空间听觉的研究成果,从染色体编码、种群的初始化、适应度函数的设计,到遗传操作操作数的设计、染色体解码等具体问题都提出了新的解决方案,如采用改进的选择方式、提出自适应遗传算法、提出精英选择策略以及提出最优引导策略。在遗传算法运行的后期阶段,对个体的适应度进行适当的放大,扩大最佳个体适应度与其他个体适应度之间的差异程度,以提高个体之间的竞争性。从实验结果可以看出改进的遗传算法的逼近效果明显优于传统的遗传算法及Prony算法。
3.耦合器是一种应用十分广泛的微波电路,它可以用于组成滤波器,例如双光纤定向耦合器组成光学梳状滤波器;在滤波器滤波以后为了把信号进行分路传输要用定向耦合器,定向耦合器是多端口的器件。本文将遗传算法用于多级分支定向耦合器的优化设计并对算法进行了改进。设计中取消了主线、分支阻抗左右对称的限制,使设计的自由度进一步加大,主、副线的特性阻抗采用优化设计方法确定,分支定向耦合器的工作带宽得到了进一步扩展;在标准遗传算法的基础上,引入了最优保存策略和自适应遗传操作,算法的性能得到了提高。仿真表明,用该方法设计的多级分支定向耦合器性能优于其他设计方法。
论文最后总结了本文的工作,并提出进一步的研究探索方向。
It has been a hot research spot to adopt genetic algorithms (GA) for optimal filter design recently. The primary research of this paper concentrates mainly on the optimization design of active filters with improved genetic algorithm and the approximation problem of head-related transfer function (HRTFs).
The thesis first expounds the related theory of genetic algorithms, such as the basic concept, components, characteristics and the improved technology of genetic algorithms. Second, it carries out some exploring research in the aspect of genetic algorithm’s optimal design on filters. The major contributions made by the research are as follows:
1. Further research into the design theory of filter. Active filters is widely applied for its advantages, such as small volume and easy integration, thus showing great significance to the improvement method of the active filters. Genetic algorithm is a probability search algorithm formed by simulating life's descendiblity and evolution process in nature; Global optimization method of the circuit parameter design, which is based on total transfer function, carries out design of circuit parameters. This thesis combines genetic algorithm and the idea of global optimization together to design the Chebyshev low pass. The results show that this idea overcomes some shortcomings of traditional methods and has obvious improvement.
2. This thesis puts forward the idea that the improved genetic algorithm approximates HRTFs. To solve the problem that there is a big error caused by the traditional genetic algorithm, this research makes use of the outcomes of space hearing and provides new solutions to chromosome coding, population initialization, the designing of fitness function and genetic operations, and decoding chromosome as well. Examples are adopting improved ways of choosing, putting forward adaptive genetic algorithm, elite selection strategy and best guide strategy. In the late period of the function of genetic algorithm, properly enlarging the degree of fitness of individuals, broadening difference between the best individual fitness and that of other individuals serve to increase the competition among individuals. As is revealed from the results of the experiment, the approximation of improved genetic algorithm is obviously better than that of the traditional algorithm or Prony.
3. Coupler is a kind of microwave circuit applied widely, which can compose filter , such as dual directional coupler can compose optical comb filter.After filtering, for the signal broadband transmission, we should use the directional coupler, which is the multi-port device. This paper uses genetic algorithm in optimum design of the multiple grade branch directional coupler and makes some improvements in algorithms. The design abandons the limit of balance between the main line and branches, which leads to strengthening the freedom of design work. The optimum design method determines the characteristic impedance of both main lines and braches, as a result of which the bandwidth of the directional coupler is broadened. Based on the standard genetic algorithm, the best storage strategy and fitness genetic operations are brought in to improve the performance of the algorithm. Simulation shows that multiple grade branch directional coupler designed with this method performs better than any other design method.
The thesis finally makes conclusions about the research that has been done and puts forward as well the direction for further research.
引文
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[2] Wightman F L,Kistler D J. Headphone simulation of free-field listening(I): Stimulus synthesis,Journal of the Acoustical Society of America,1989,85(2):858-867
[3] Kister D,Wightman F.A model of HRTFs based on principal components analysis and minimum-phase reconstruction. Journal of the Acoustical Society of America 1992, 91(3):1637-1647
[4] Net C,Young E D,Schneider M H.Neural network model of sound localization based on directional filtering by the Pinna.Journal of the Acoustical Society of America, 1992,92(6):3140-3156
[5] R.L.Geiger and E.Sanchez-Sinencio. Active filter design using operational transconductance amplifiers: a tutorial[J]. IEE Circuits Devices Meg,1985,2(1): 20-32.
[6] Deczky A G. Synthesis of recursive digital filters using the minimum P-error criterion. IEEE Trans. Audio Electroacoust,1972,20:257-263
[7] Alliney S,Sgallari F. Chebyshev approximation of recursive digital filters having specified amplitude and phase characteristics. Signal Processing,1980,2(4): 317-321
[8] Gutknecht M H,etal.The caratheodory-fejer method for recursive digital design. IEEE Trans on ASSP,1983,31:1417-1426
[9] Kobayashi T,Imai S.Design of IIR digital filters with arbitrary log magnitude function by WLS echniques,IEEE Trans on ASSP,1990,38(2):247-252
[10] Chen X,Parks T W.Design of IIR filters in the complex domain.IEEE Trans ASSP 1990,38(6):910-920
[11] Shaw A K. Optimal design of digital IIR filter by model-fitting frequency response data. In:1993 IEEE Int Symposium On Circuits and Systerms,1993,475-478
[12]李尧.进化型模拟滤波器的研究.硕士学位论文.长春:东北师范大学,2005.
[13]刘勇,康立山,陈毓屏.非数值并行算法(第二册)—遗传算法[M].北京:科学出版社,1995.
[14]陈国良,王煦法,庄镇泉等.遗传算法及其应用[M].北京:人民邮电出版社,1996.112-113.
[15] Garis H D. Evolvable Hardware Genetic Programming of a Darwin Machine in:Branko Soucek and the IRIS Group (Eds.),Dynamic,Genetic and Chaotic Programming[J]. John Wiley&Sons, Inc,1992,373-393.
[16]彭新竹,遗传算法的改进策略及其应用[J].华东船舶工业学院学报(自然科学版),2002,16(3): 53-58
[17]鞠艳杰.进化型模拟有源滤波器的研究.硕士学位论文.长春:东北师范大学,2004.
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