课程设计-基于Blackman窗的FIR数字低通滤波器设计.doc

课 程 设 计课程设计名称:基于Blackman窗的FIR数字低通滤波器设计专业班级 ： 电信1003 学生姓名 ： 星空 学 号 ： 指 导 教 师 ： 课程设计时间： 2013.6.24-2013.6.30 数字信号处理 专业课程设计任务书学生姓名星空专业班级电信1003学号题 目基于Blackman窗的FIR数字低通滤波器设计课题性质工程技术研究课题来源自拟课题指导教师同组姓名主要内容 设计一个具有如下性能指标的FIR数字带通滤波器：=0.25，=0.4；窗函数为Blackman窗；分析最后设计结果性能。任务要求1. 温习窗函数法设计数字FIR滤波器的原理和设计方法；2. 求出最后所设计出的滤波器冲激响应系数；3. 绘制所设计滤波器的增益响应曲线。参考文献1 胡广书. 数字信号处理理论、算法与实现M. 北京: 清华大学出版社, 1997.2 R. Lyons. Understanding Digital Signal Processing M. 2nd ed. Prentice Hall PTR., 2004.3 A.V.奥本海姆, R.W.谢弗 and J.R.巴克. 离散时间信号处理M. 第二版. 西安交通大学出版社, 2001.4 S. K. Mitra. Digital Signal Processing: A Computer-Based ApproachM. 3rd ed. McGraw-Hill, 2005.审查意见指导教师签字：李相国教研室主任签字： 年 月 日 说明：本表由指导教师填写，由教研室主任审核后下达给选题学生，装订在设计（论文）首页1 需求分析数字滤波器可以理解为是一个计算程序或算法，将代表输入信号的数字时间序列转化为代表输出信号的数字时间序列，并在转化过程中，使信号按预定的形式变化。数字滤波器有多种分类，根据数字滤波器冲激响应的时域特征，可将数字滤波器分为两种，即无限长冲激响应（iir）滤波器和有限长冲激响应（fir）滤波器。iir数字滤波器具有无限宽的冲激响应，与模拟滤波器相匹配。所以iir滤波器的设计可以采取在模拟滤波器设计的基础上进一步变换的方法。fir数字滤波器的单位脉冲响应是有限长序列。它的设计问题实质上是确定能满足所要求的转移序列或脉冲响应的常数问题，设计方法主要有窗函数法、频率采样法和等波纹最佳逼近法等。因此设计FIR滤波器的方法之一可以从时域出发，截取有限长的一段冲击响应作为H(z)的系数，冲击响应长度N就是系统函数H(z)的阶数。只要N足够长，截取的方法合理，总能满足频域的要求。一般这种时域设计、频域检验的方法要反复几个回合才能成功。要设计一个线性相位的FIR数字滤波器，首先要求理想频率响应。是w的周期函数，周期为，可以展开成傅氏级数： 其中是与理想频响对应的理想单位抽样响应序列。但不能用来作为设计FIR DF用的h(n)，因为一般都是无限长、非因果的，物理上无法实现。为了设计出频响类似于理想频响的滤波器，可以考虑用h(n)来近似。窗函数的基本思想：先选取一个理想滤波器（它的单位抽样响应是非因果、无限长的），再截取（或加窗）它的单位抽样响应得到线性相位因果FIR滤波器。这种方法的重点是选择一个合适的窗函数和理想滤波器。设x(n)是一个长序列，w(n)是长度为N的窗函数，用w(n)截断x(n)，得到N点序列xn(n)，即xn(n) = x(n) w(n) 在频域上则有 由此可见，窗函数w(n)不仅仅会影响原信号x(n)在时域上的波形，而且也会影响到频域内的形状。加矩形窗后的频谱和理想频谱可得到以下结论：加窗使过渡带变宽，过渡带的带宽取决于窗谱的主瓣宽度。矩形窗情况下的过渡带宽是。N越大，过渡带越窄、越陡；过渡带两旁产生肩峰，肩峰的两侧形成起伏振荡。肩峰幅度取决于窗谱主瓣和旁瓣面积之比。矩形窗情况下是8.95，与N无关。工程上习惯用相对衰耗来描述滤波器，相对衰耗定义为 这样两个肩峰点的相对衰耗分别是0.74dB和-21dB。其中（-0.0895）对应的点的值定义为阻带最小衰耗。以上的分析可见，滤波器的各种重要指标都是由窗函数决定，因此改进滤波器的关键在于改进窗函数。窗函数谱的两个最重要的指标是：主瓣宽度和旁瓣峰值衰耗。旁瓣峰值衰耗定义为： 旁瓣峰值衰耗20lg(第一旁瓣峰值主瓣峰值) 为了改善滤波器的性能，需使窗函数谱满足：主瓣尽可能窄，以使设计出来的滤波器有较陡的过渡带；第一副瓣面积相对主瓣面积尽可能小，即能量尽可能集中在主瓣，外泄少，使设计出来的滤波器的肩峰和余振小。但上面两个条件是相互矛盾的，实际应用中，折衷处理，兼顾各项指标。本次设计要求以窗函数为Blackman窗为基础，设计一个具有如下性能指标的FIR数字带通滤波器： =0.25，=0.4 2 概要设计如果所希望的滤波器的理想的频率响应函数为，则其对应的单位脉冲响应为窗函数设计法的基本原理是用有限长单位脉冲响应序列逼近。由于往往是无限长序列，而且是非因果的，所以用窗函数将截断，并进行加权处理，得到：就作为实际设计的FIR数字滤波器的单位脉冲响应序列，其频率响应函数为式中，N为所选窗函数的长度。我们知道，用窗函数法设计的滤波器性能取决于窗函数的类型及窗口长度N的取值。设计过程中，要根据对阻带最小衰减和过渡带宽度的要求选择合适的窗函数类型和窗口长度N 。主程序框图如图4.1所示。其中幅度特性要求用dB表示。开始计算并读入窗口长度N计算hd(n)调用窗函数子程序求w(n)调用子程序（函数）计算H(k)=DFTh(n)调用绘图子程序（函数）绘制H(k)幅度相位曲线结束图1 主程序框图计算h(n)= hd(n) w(n)布莱克曼窗函数布莱克曼窗函数的时域形式可以表示为 它的频域特性为：其中，为矩形窗函数的幅度频率特性函数。布莱克曼窗函数的最大旁瓣值比主瓣值低57dB，但是主瓣宽度是矩形窗函数的主瓣宽度的3倍，为12/N。Blackman函数调用方式： w = blackman (n)：输入参数n是窗函数的长度；输出参数w是由窗函数的值组成的n阶向量。3 运行环境软件环境：1.Windows xp2. MATLAB6.54 开发工具和编程语言开发工具:MATLAB桌面和命令窗口、历史命令窗口、编辑器和调试器、路径搜索和用于用户浏览帮助、工作空间、文件的浏览器。MATLAB一个高级的矩阵/阵列语言，它包含控制语句、函数、数据结构、输入和输出和面向对象编程特点。用户可以在命令窗口中将输入语句与执行命令同步，也可以先编写好一个较大的复杂的应用程序（M文件）后再一起运行。5 详细设计 算法实现的源程序：（1）计算实际滤波器的幅度，相位响应function db,mag,pha,grd,w=myfreqz(b,a); N=1000;H,w=freqz(b,a,N,whole);H=(H(1:1:501);w=(w(1:1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag);pha=angle(H);grd=grpdelay(b,a,w); （2）求滤波器的理想脉冲响应function hd=ideal_lp(wc,M);al=(M-1)/2;n=0:(M-1);m=n-al+eps;hd=sin(wc*m)./(pi*m);（3）主程序：wst=0.4*pi;wp=0.25*pi;deltaw=wst-wp; %过渡带宽w的计算N0=ceil(11*pi/deltaw); %按布莱克曼窗计算所需的滤波器长度N=N0+mod(N0+1,2);%为了实现第一类偶对称滤波器，应确保其长度N为奇数n=0:1:N-1;wc=(wst+wp)/2; %截止频率取为两边缘频率的平均值hd=ideal_lp(wc,N); %求理想脉冲响应wdbla=(blackman(N); %求窗函数h=hd.*wdbla; %设计的脉冲响应应为理想脉冲响应与窗函数乘积db,mag,pha,grd,w=myfreqz(h,1); %对设计结果进行检验dw=2*pi/2000; %频率分辨率Rp=-(min(db(1:wp/dw+1) %检验通带波动As=-round(max(db(wst/dw+1:501) %检验最小阻带衰减figure(1)subplot(2,2,1);stem(n,wdbla);title(布莱克曼窗) %绘制布莱克曼窗axis(0 N-1 0 1.1);ylabel(w(n);text(N+1,0,n)subplot(2,2,2);stem(n,h);title(实际脉冲响应) %绘制实际脉冲响应axis(0 N-1 -0.4 0.5);xlabel(n);ylabel(h(n)subplot(2,2,3);plot(w/pi,db); %绘制幅度响应;title(幅度响应（单位：dB);grid;axis(0 1 -150 10);xlabel(频率（单位： pi);ylabel(分贝数)set(gca,XTickMode,manual,XTick,0,0.2,0.35,0.65,0.8,1)set(gca,YTickMode,manual,YTick,-60,0)subplot(2,2,4);plot(w,pha);title(相位响应); %绘制相频特性axis(0 2 -4 4);xlabel(频率（单位:pi);ylabel(相位()6 调试分析设计低通滤波器时首先要计算出过渡带宽，然后查表得到所设计窗函数所需要的阶数，不同的窗函数所设计的滤波器的形状各有差异，尤其在主瓣宽度、旁瓣的形状以及主瓣与旁瓣的高度差上有比较明显得差别，实际应用中应根据实际情况，折衷处理，兼顾各项指标。实际中遇到的离散时间信号总是有限长的，因此不可避免地要遇到数据截断问题。而在信号处理中，对离散序列的数据截断是通过序列与窗函数相乘来实现的。7 测试结果测试结果有错，初始参数为ws=0.4*pi;wp=0.25*pi，运行出错，错误在主程序最后一行：axis(0 2 -4 4);xlabel(频率（单位:pi);ylabel(相位()，最后检查出来为标点出错，应为英文输入法下的标点运行结果(图):参考文献1刘泉 信号与系统 高等教育出版社 2006 2 丁玉美，高西全编著. 数字信号处理.西安：西安电子科技大学出版社，20003刘泉 数字信号处理原理与实现 电子工业出版社 20054 黄文梅，熊桂林，杨勇编著. 信号分析与处理-MATLAB语言及应用.长沙：国防科技大学出版社5 张宗橙，张玲华，曹雪虹编著. 数字图像处理与应用。南京：东南大学出版社，1997心得体会通过对该课程的学习，我对数字通信理论有了更进一步的理解；通过对该数字滤波器的设计，我也了解了数字滤波器的基本结构和基本特性，而且还掌握了基本的撰写论文的形式和思路。作为一个电子信息工程专业的学生，数字信号处理是我们的重要专业课程，是我们将来从事通信事业的基本保障。通过对作为该论文的重要部分MATLAB的运用，大大提高了我们对集计算，编程与绘图于一体的该应用软件的运用能力。MATLAB包含的几十个工具箱，覆盖了通信，自动控制，信号处理，图象处理，财经，化工，生命科学等科学技术领域，汲取了当今世界这些领域的最新研究成果，已经成为从事科学研究和工程设计不可缺少的工具软件。该课程设计将数字信号处理的有关教学内容和MATLAB语言紧密，有机地结合起来，使我们在学习基础理论知识的同时学会了应用MATLAB，在学习应用MATLAB的同时，加深了对基本知识的理解，增强了我们的计算机应用能力，提高了学习效果。总之，无论是从教学知识掌握出发，还是从对MATLAB的应用出发，通过这次学习，我不但掌握了基于Blackman窗的FIR数字带通滤波器设计的基本知识及其实际应用的技巧，还提高了自己的编程和写报告的能力，收获不小,也巩固了所学知识。 g an employment tribunal claimEmployment tribunals sort out disagreements between employers and employees.You may need to make a claim to an employment tribunal if: you dont agree with the disciplinary action your employer has taken against you your employer dismisses you and you think that you have been dismissed unfairly.For more information about dismissal and unfair dismissal, seeDismissal.You can make a claim to an employment tribunal, even if you haventappealedagainst the disciplinary action your employer has taken against you. However, if you win your case, the tribunal may reduce any compensation awarded to you as a result of your failure to appeal.Remember that in most cases you must make an application to an employment tribunal within three months of the date when the event you are complaining about happened. If your application is received after this time limit, the tribunal will not usually accept it.If you are worried about how the time limits apply to you, take advice from one of the organisations listed underFurther help.Employment tribunals are less formal than some other courts, but it is still a legal process and you will need to give evidence under an oath or affirmation.Most people find making a claim to an employment tribunal challenging. If you are thinking about making a claim to an employment tribunal, you should get help straight away from one of the organisations listed underFurther help.If you are being represented by a solicitor at the tribunal, they may ask you to sign an agreement where you pay their fee out of your compensation if you win the case. This is known as adamages-based agreement. In England and Wales, your solicitor cant charge you more than 35% of your compensation if you win the case.If you are thinking about signing up for a damages-based agreement, you should make sure youre clear about the terms of the agreement. It might be best to get advice from an experienced adviser, for example, at a Citizens Advice Bureau. To find your nearest CAB, including those that give advice by e-mail, click onnearest CAB.For more information about making a claim to an employment tribunal, seeEmployment tribunals.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA.Age has reached the end of the beginning of a word. May be guilty in his seems to passing a lot of different life became the appearance of the same day; May be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind has been very messy, in my mind constantly. Always feel oneself should go to do something, or write something. Twenty years of life trajectory deeply shallow, suddenly feel something, do it.一字开头的年龄已经到了尾声。或许是愧疚于自己似乎把转瞬即逝的很多个不同的日子过成了同一天的样子；或许是追溯过去，对自己那些近乎偏执的怪异信念的醒悟，这些天以来，思绪一直很凌乱，在脑海中不断纠缠。总觉得自己自己似乎应该去做点什么，或者写点什么。二十年的人生轨迹深深浅浅，突然就感觉到有些事情，非做不可了。The end of our life, and can meet many things really do?而穷尽我们的一生，又能遇到多少事情是真正地非做不可？During my childhood, think lucky money and new clothes are necessary for New Year, but as the advance of the age, will be more and more found that those things are optional; Junior high school, thought to have a crush on just means that the real growth, but over the past three years later, his writing of alumni in peace, suddenly found that isnt really grow up, it seems is not so important; Then in high school, think dont want to give vent to out your inner voice can be in the high school children of the feelings in a period, but was eventually infarction when graduation party in the throat, later again stood on the pitch he has sweat profusely, looked at his thrown a basketball hoops, suddenly found himself has already cant remember his appearance.童年时，觉得压岁钱和新衣服是过年必备，但是随着年龄的推进，会越来越发现，那些东西根本就可有可无；初中时，以为要有一场暗恋才意味着真正的成长，但三年过去后，自己心平气和的写同学录的时候，突然就发现是不是真正的成长了，好像并没有那么重要了；然后到了高中，觉得非要吐露出自己的心声才能为高中生涯里的懵懂情愫划上一个句点，但毕业晚会的时候最终还是被梗塞在了咽喉，后来再次站在他曾经挥汗如雨的球场，看着他投过篮球的球框时，突然间发现自己已经想不起他的容颜。Originally, this world, can produce a chemical reaction to an event, in addition to resolutely, have to do, and time.原来，这个世界上，对某个事件能产生化学反应的，除了非做不可的坚决，还有，时间。A persons time, your ideas are always special to clear. Want, want, line is clear, as if nothing could shake his. Also once seemed to be determined to do something, but more often is he backed out at last. Dislike his cowardice, finally found that there are a lot of love, there are a lot of miss, like shadow really have been doomed. Those who do, just green years oneself give oneself an arm injection, or is a self-righteous spiritual.一个人的时候，自己的想法总是特别地清晰。想要的，不想要的，界限明确，好像没有什么可以撼动自己。也曾经好像已经下定了决心去做某件事，但更多的时候是最后又打起了退堂鼓。嫌恶过自己的怯懦，最终却发现有很多缘分，有很多错过，好像冥冥之中真的已经注定。那些曾经所谓的非做不可，只是青葱年华里自己给自己注射的一支强心剂，或者说，是自以为是的精神寄托罢了。At the moment, the sky is dark, the air is fresh factor after just rained. Suddenly thought of blue plaid shirt; Those were broken into various shapes of stationery; From the corner at the beginning of deep friendship; Have declared the end of the encounter that havent start planning. Those years, those days of do, finally, like youth, will end in our life.此刻，天空是阴暗的，空气里有着刚下过雨之后的清新因子。突然想到那件蓝格子衬衫；那些被折成各种各样形状的信纸；那段从街角深巷伊始的友谊；还有那场还没有开始就宣告了终结的邂逅计划那些年那些天的非做不可，终于和青春一样，都将在我们的人生中谢幕。Baumgartner the disappointing news: Mission aborted. r plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The supersonic descent could happen as early as Sunda.The weatheThe balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto so