汉宁窗的matlab实现.doc

数字信号处理课程设计题目：用汉宁窗设计FIR数字低通滤波器对给定数据进行滤波 院系： 专业：通 信 工 程 班级: 学号: 姓名: 指导教师: 职称: 1.1 FIR滤波器:有限长单位脉冲响应数字滤波器（Finite Impulse Response Digital Filter,缩写FIRDF）：有限长单位冲激响应滤波器，是数字信号处理系统中最基本的元件，最大优点是可以实现线性相性滤波，它可以在保证任意幅频特性的同时具有严格的线性相频特性，同时其单位抽样响应是有限长的，因而滤波器是稳定的系统。因此，FIR滤波器在通信、图像处理、模式识别等领域都有着广泛的应用。FIR滤波器的设计方法主要分为两类：第一类是基于逼近理想滤波器器特性的方法包括窗函数法、频率采样法、和等波纹最佳逼近法；第二类是最优设计法。设FIRDF的单位脉冲响应的长度为，则其频率响应函数为 （1-1）一般将表示成如下形式： （1-2）式中，是的实函数（可以去负值）。与前面的表示形式，即相比， 与不同。与 不同。为了区别于幅频响应函数和相频响应函数，称为幅频特性函数，称为相频特性函数。第一类线性相位FIRDF的相位特性函数是的严格线性函数： （1-3）第二类线性相位FIRDF的相位特性函数如下： （1-4）式中，是常数，是起始相位。在信号处理中很有实用价值（如希伯尔特变换器），这是FIRDF除了线性相位滤波外，还具有真正交变换作用。1.2 窗函数设计法：窗函数设计法的基本思想是用FIRDF逼近希望的滤波特性。设希望逼近的滤波器的频率响应为，其单位脉冲响应用表示。为了设计简单方便，通常选择为具有片段常数特性的理想滤波器。因此是无限长非因果序列，不能直接作为FIRDF的单位脉冲响应。窗函数设计法就是截取为有限长的一段因果序列，并用合适的窗口函数进行加权作为FIRDF的单位脉冲响应。常见的窗函数，可以分为以下主要类型，（1） 幂窗-采用时间变量某种幂次的函数，如矩形、三角形、梯形或其它时间（t）的高次幂； （2）三角函数窗-应用三角函数，即正弦或余弦函数等组合成复合函数，例如汉宁窗、海明窗等；（3） 指数窗-采用指数时间函数，例如高斯窗等5。其性能如表1-1所示：名称滤波器过渡带宽最小阻带衰减名称滤波器过渡带宽最小阻带衰减矩形1.8/M21dBPARZENWIN6.6/M56db巴特利特6.1/M25dBFLATTOPWIN19.6/M108db汉宁6.2/M44dBGAUSSWIN5.8/M60db汉明6.6/M51dBBARTHANNWIN3.6/M40db布莱克曼11/M74dBBLACKMANHARRIS16.1/M109dbBOHMANWIN5.8/M51.5dbCHEBWIN15.2/M113dbNUTTALLWIN15.4/M108dbTUKEYWIN2.4/M22db表1-1 常见窗函数性能表用窗口设计法基本步骤如下：（1）构造希望逼近的频率响应函数。以低通线性相位FIRDF设计为例，一般选择为线性理想低通滤波器，即 （1-5）（2）求出。对进行IFT得到 （1-6）（3）加窗得到FIRDF的单位脉冲响应， （1-7）式中，称为窗口函数，其长度为。如果要求第一类线性相位FIRDF，则要求关于点偶对称。而关于点偶对称，所，同时要求关于点偶对称。1.3 汉宁窗：汉宁窗（Hanning Window）又称升余弦窗，汉宁窗可以看作是3个矩形时间窗的频谱之和，或者说是3个型函数之和，而括号中的两项相对于第一个谱窗向左、右各移动了/T，从而使旁瓣互相抵消，消去高频干扰和漏能。可以看出，汉宁窗主瓣加宽并降低，旁瓣则显著减小，从减小泄漏观点出发，汉宁窗优于矩形窗但汉宁窗主瓣加宽，相当于分析带宽加宽，频率分辨力下降。 （1-8）根据傅里叶变换的线性性质和调制定理得到（1-9）当时，则 （1-10）为汉宁窗的幅度响应函数。二、设计流程图： 本课程设计主要是对一段数据，加入噪声后，用汉宁窗函数法设计出的FIR滤波器对加入噪声后的数据信号进行滤波去噪处理，并且分析对比前后时域和频域波形的程序设计。程序的设计流程图如下图2-1所示：从文本中读取数据信号对输入信号进行频谱分析，画出频域波形图 用汉宁窗设计FIR滤波器画出其频率响应用FIR滤波器对数字信号进行滤波画出数字信号滤波前后波形并且进行比较分析开始结束实际滤波器单位冲击响应图2-1 程序设计流程图三、matlab设计函数及结果：用汉宁窗设计的FIR数字低通滤波器的程序（含界面）：function varargout = hanning(varargin)% HANNING M-file for hanning.fig% HANNING, by itself, creates a new HANNING or raises the existing% singleton*.% H = HANNING returns the handle to a new HANNING or the handle to% the existing singleton*.% HANNING(CALLBACK,hObject,eventData,handles,.) calls the local% function named CALLBACK in HANNING.M with the given input arguments.% HANNING(Property,Value,.) creates a new HANNING or raises the% existing singleton*. Starting from the left, property value pairs are% applied to the GUI before hanning_OpeningFunction gets called. An% unrecognized property name or invalid value makes property application% stop. All inputs are passed to hanning_OpeningFcn via varargin.% *See GUI Options on GUIDEs Tools menu. Choose GUI allows only one% instance to run (singleton).% See also: GUIDE, GUIDATA, GUIHANDLES % Edit the above text to modify the response to help hanning % Last Modified by GUIDE v2.5 29-Jun-2011 11:03:04 % Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct(gui_Name, mfilename, . gui_Singleton, gui_Singleton, . gui_OpeningFcn, hanning_OpeningFcn, . gui_OutputFcn, hanning_OutputFcn, . gui_LayoutFcn, , . gui_Callback, );if nargin & ischar(varargin1) gui_State.gui_Callback = str2func(varargin1);end if nargout varargout1:nargout = gui_mainfcn(gui_State, varargin:);else gui_mainfcn(gui_State, varargin:);end% End initialization code - DO NOT EDIT % - Executes just before hanning is made visible.function hanning_OpeningFcn(hObject, eventdata, handles, varargin)global xn;global hj1;global hj2;% This function has no output args, see OutputFcn.% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to hanning (see VARARGIN)hj1=load(E:a.txt);xn=hj1;% Choose default command line output for hanninghandles.output = hObject; % Update handles structureguidata(hObject, handles); % UIWAIT makes hanning wait for user response (see UIRESUME)% uiwait(handles.hanning_gui); % - Outputs from this function are returned to the command line.function varargout = hanning_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structurevarargout1 = handles.output; function edt_wp_Callback(hObject, eventdata, handles)% hObject handle to edt_wp (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,String) returns contents of edt_wp as text% str2double(get(hObject,String) returns contents of edt_wp as a double % - Executes during object creation, after setting all properties.function edt_wp_CreateFcn(hObject, eventdata, handles)% hObject handle to edt_wp (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc & isequal(get(hObject,BackgroundColor), get(0,defaultUicontrolBackgroundColor) set(hObject,BackgroundColor,white);end function edt_ws_Callback(hObject, eventdata, handles)% hObject handle to edt_ws (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,String) returns contents of edt_ws as text% str2double(get(hObject,String) returns contents of edt_ws as a double % - Executes during object creation, after setting all properties.function edt_ws_CreateFcn(hObject, eventdata, handles)% hObject handle to edt_ws (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc & isequal(get(hObject,BackgroundColor), get(0,defaultUicontrolBackgroundColor) set(hObject,BackgroundColor,white);end % - Executes on button press in btn_creat.function btn_creat_Callback(hObject, eventdata, handles)global xn;global hj1;global hj2;% hObject handle to btn_creat (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) H=findobj(Tag,edt_wp);aaa=get(H, string);wp=str2num(aaa)*pi;H=findobj(Tag,edt_ws);aaa=get(H, string);ws=str2num(aaa)*pi; deltaw=ws-wp;N0=ceil(6.2*pi/deltaw);N=N0+mod(N0+1,2);n=0:N-1;wn=0.5*(1-cos(2*pi*n/(N-1);wc=(ws+wp)/2;nn=(N-1)/2;hd=sin(wc*(n-nn)+eps)./(pi*(n-nn)+eps);h=hd.*wn; H,w=freqz(h,1,1000,whole);H=(H(1:1:501);w=(w(1:1:501);mag=abs(H); %绝对幅值响应db=20*log10(mag+eps)/max(mag); %相对幅值响应pha=angle(H); %相位响应 yn=conv(xn,h); axes(handles.axes1);plot(h);grid;title(实际单位冲击响应);axes(handles.axes2);plot(w/pi,db);grid;title(汉宁窗滤波器的幅频特性);axes(handles.axes3);plot(w/pi,pha);grid;title(汉宁窗滤波器的相频特性);axes(handles.axes4);plot(xn);grid;title(输入信号);axes(handles.axes5);plot(yn);grid;title(输出信号); % - Executes on button press in btn_zero.function btn_zero_Callback(hObject, eventdata, handles)% hObject handl