DSP滤波器中英文对照外文翻译文献

中英文对照外文翻译文献

(文档含英文原文和中文翻译)

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译文:

GA算法优化IIR滤波器的设计

摘要 本文提出了运用遗传算法(GA)来优化无限脉冲响应数字滤波器(IIR)的设计。

IIR滤波器本质上是一个递归响应的数字滤波器。由于IIR数字滤波器的表面误差通常是非线性的和多峰的，而全局优化技术需要避免局部最小值。本文提出了启发式方式来设计IIR滤波器。GA是组合优化问题中一种功能强大的全局优化算法，该论文发现IIR数字滤波器的最佳系数可以通过GA优化。该设计提出低通和高通IIR数字滤波器的设计，以提供过渡频带的估计值。结果发现，所计算出的值比可用于过滤器的在MATLAB设计FDA工具更优化。举个例子，采用的仿真结果表明在过渡带和均方误差(MSE)的改善。零极点的位置也被提出来用来描述系统的的稳定性，以便将结果与模拟退火(SA)的方法相比较。

关键词：数字滤波器;无限冲激响应(IIR);遗传算法(GA);优化 1.说明

在过去的几十年中的数字信号处理(DSP)领域已经成长太重要的理论和技术。在DSP中，有两个重要的类型系统。第一类型的系统是执行信号滤波的时域，因此它被称为数字滤

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波器。第二类型的系统提供的信号表示频域，被称为频谱分析仪。数字滤波是DSP的最有力的工具之一。数字滤波器能够性能规格，最好的同时也是极其困难的，而且不可能的是，先用模拟滤波器实现。另外，数字滤波器的特性，可以很容易地在软件控制下发生变化。数字滤波器被分类为有限持续时间脉冲响应(FIR)滤波器或无限持续时间脉冲响应(IIR)滤波器，这取决于该系统的脉冲响应的形式。在FIR系统中，脉冲响应序列是有限的持续时间，即，它具有非零项的数量有限。数字无限脉冲响应(IIR)滤波器通常可以提供比其等效有限脉冲响应(FIR)滤波器更好的性能和更少的计算成本，并已成为越来越感兴趣的目标。

但是，由于IIR滤波器的误差表面通常是非线性的，多式联运，传统的基于梯度的设计方法可以很容易地陷入错误的表面。因此当地极小，一些研究者已经试图开发基于设计方法现代启发式优化算法，如遗传算法(GA)，模拟退火(SA)，禁忌搜索(TS).简单的迭代方法通常导致次优的设计。因此，有必要的优化方法(启发式型)，可以是用来设计数字滤波器，将满足规定的规格。古德伯格呈现遗传算法的详细的数学模型。本韦努托切在书中描述在设计数字滤波器具有线性相位数字滤波器的上下文中使用模拟退火(SA)算法的显着特征。该算法然后被应用到FIR滤波器的设计。其结果是并不令人印象深刻。此外，它在计算上的花费是非常昂贵的。

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艾哈迈德用遗传算法设计与CSD系数限制的低通滤波器的一阶IIR滤波器。艾哈迈德和安东尼屋探讨了FIR滤波器和均衡器，通过遗传算法的使用，因而气需要大量的计算。2007年奥利维拉等人提出了利用非线性随机全局优化的模拟退火技术，设计基于线性FIR滤波器的一种新方法。2011年维斯和唐评价了遗传编程(GP)的适用性的分布式算法的进化。上述各种方法的基本限制是它们主要是用来设计FIR数字滤波器。前面的设计方法的缺点是计算时间是相当长的测试优化方法，所提出的算法在MATLAB和实现的结果是非常令人鼓舞的。本文的组织如下：在第2节中，IIR数字滤波器的设计问题进行了讨论。在3节中，遗传算法(GA)的方法作了简要的阐述。遗传算法(GA)对滤波器的设计是在4节中提出了相关的。设计实例的仿真结果进行简要描述在5节。结论和未来的范围是在6节中描述的。响应IIR滤波器的递推或是依赖于一个或更多的过去的输出。如果这样的过滤器进行一个脉冲的输出不一定为零。这表明，系统很容易反馈和不稳定。每个解决方案与健身价值，反映了它是多么的好，在人群中有[ 16 ]其他方案进行了比较。通过交叉机制，交流部分之间的数据字符串模拟染色体重组过程。新的遗传物质也通过突变导致的随机变化的字符串了。对这些遗传操作的发生频率是由一定的概率控制。的选择，交叉，变异过程如图2所示[ 17 ]构成的基本遗传算法的循环或生成，这是重复

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直到预定的标准是满意的。通过这一过程，先后更好个体的物种生成。随着计算能力的集成电路技术的进步提供了进化系统，仿真越来越听话的气被应用到许多现实世界的问题，包括数字滤波器的设计。

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原文:

Genetic Algorithm for the Design of Optimal IIR

Digital Filters

ABSTRACT

This paper presents the design of Optimal Infinite-Impulse Response (IIR) digital filters using Genetic Algorithm (GA).

IIR filter is essentially a digital filter with Recursive responses. Since the error surface of digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. This paper presents heuristic way for the designing IIR filters. GA is a powerful global optimization algorithm introduced in combinatorial optimization problems. The paper finds the optimum Coefficients of IIR digital filter through GA. Design of

Low pass and High pass IIR digital filter is proposed to provide estimate of transition band. It is found that the calculated values are more optimal than fda tool available for the design of filter in MATLAB. The simulation result of the employed examples shows an improvement on transition band and mean-square-error (MSE). The position of pole-zero is also presented to describe stability and results are compared with Simulated Annealing (SA) method.

Keywords: Digital Filter; Infinite-Impulse Response (IIR); Genetic Algorithm (GA); Optimization

1. Introduction

1. Over the last few decades the field of Digital Signal Processing (DSP) has grown to important both theoretically and technologically. In DSP, there are two important types of Systems. The first

2.type of systems performs signal filtering in time domain and hence it is known as Digital filters. The second type of systems provide signal representation frequency domain and are known as Spectrum Analyzer. Digital filtering is one of the most powerful tools of DSP. Digital filters are capable of performance specifications that would, at best, be extremely difficult, if not impossible, to achieve with an analog implementation. In addition, the characteristics of a digital filter can be easily changed under software control. Digital filters are classified either as Finite duration impulse response (FIR) filters or Infinite duration impulse response (IIR) filters, depending on the form of impulse response of the system. In the FIR system, the impulse response sequence is of finite duration, i.e., it has a finite number of non zero terms. Digital infinite-impulse-response (IIR) filters can often provide a much better performance and less computational cost than their equivalent finite-impulse-response (FIR) filters and have become the target of growing interest . However, because the error surface of IIR filters is usually nonlinear and multimodal, conventional gradient-based design methods may easily get stuck in the local minima of error surface.Therefore, some researchers have attempted to develop design

methods based on modern heuristic optimization algorithms such as genetic algorithm (GA) , simulated annealing (SA), tabu search (TS) .Analytical or simple iterative methods usually lead to sub-optimal designs. Consequently, there is a need of optimization methods (heuristic type) that can be use to design digital filters that would satisfy prescribed specifications. Goldberg presented a detailed mathematical model of Genetic Algorithm . Benvenuto et al. (1992) described the salient features of using a simulated annealing (SA) algorithm in the context of designing digital filters with linear phase digital filter. The algorithm is then applied to the design of FIR filter. The result was not impressive. Moreover, it is computationally very expensive. Ahmadi et al.(2003) used genetic algorithm to design 1-D IIR filter with canonical-signed-digit coefficients restricted to low-pass filter. Ahmad and Antoniou (2006) explored FIR filters and equalizers through the use of GA. Consequently GAs requires a large amount of computation. Oliveira et al. (2007) presented a new approach for designing linear FIR filters by using nonlinear stochastic global optimization based on simulated annealing techniques. Jung et al. (2008) found the design method of a linear phase finite word length finite-duration impulse response (FIR) filter using simulated annealing. Weise and Tang (2011) evaluated the applicability of genetic programming (GP) for the evolution of distributed algorithms. The basic limitation of all the above methods is that they can mainly be used to design FIR digital filters. The drawback of preceding design methods is that the computation time is quite long To test the optimization procedure, the proposed algorithm is implemented in Matlab and results are found to be very encouraging. This Paper is organized as follows: In Section 2, IIR digital filter design aspects are

discussed. In section 3,Genetic Algorithm (GA) approach is briefly mentioned.The Genetic Algorithm (GA) related to filter design is proposed in Section 4. The simulation results of designed examples used is briefly described in Section 5. The Conclusion and future scope is described in Section 6. 2. IIR Filter Design Issues Digital filters are classified as Recursive and Non-Re- cursive filters. The response of Recursive or IIR filters is dependent on one or more of its past output. If such filter subjected to an impulse then its output need not necessarily become zero. This indicates that the system is prone to feedback and instability. mechanism for better solutions to survive. Each solutions associated with a fitness value that reflects how good it is, compared with other solutions in the population .The recombination process is simulated through a cross-over mechanism that exchanges portions of data strings between the chromosomes. New genetic material is also introduced through mutation that causes random alterations of the strings. The frequency of occurrence of these genetic operations is controlled by certain preset probabilities. The selection, crossover, and mutation processes as illustrated in Figure 2 constitute the basic GA cycle or generation, which is repeated until some predetermined criteria are satisfied. Through this process, successively better and better individuals of the species are generated. With the increasing computing power offered by advancement in integrated circuit technology, the simulation of evolutionary systems is becoming more and more tractable and GAs are being applied to many real world problems including the design of digital filters.

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