(完整word版)漢寧窗的matlab實(shí)現(xiàn)

1、數(shù)字信號(hào)處理課程設(shè)計(jì)題目：用漢寧窗設(shè)計(jì)FIR數(shù)字低通濾波器對(duì)給定數(shù)據(jù)進(jìn)行濾波院系：專業(yè)： 通信工程班級(jí):學(xué)號(hào)：姓名:指導(dǎo)教師:職稱:1.1 FIR濾波器:有限長(zhǎng)單位脈沖響應(yīng)數(shù)字濾波器(Finite Impulse ResponseDigital Filter,縮寫FIRDF):有限長(zhǎng)單位沖激響應(yīng)濾波器，是 數(shù)字信號(hào)處理系統(tǒng)中最基本的元件，最大優(yōu)點(diǎn)是可以實(shí)現(xiàn)線性相 性濾波，它可以在保證任意幅頻特性的同時(shí)具有嚴(yán)格的線性相頻 特性，同時(shí)其單位抽樣響應(yīng)是有限長(zhǎng)的，因而濾波器是穩(wěn)定的系 統(tǒng)。因此，F(xiàn)IR濾波器在通信、圖像處理、模式識(shí)別等領(lǐng)域都有 著廣泛的應(yīng)用。FIR濾波器的設(shè)計(jì)方法主要分為兩類：第一類是

2、 基于逼近理想濾波器器特性的方法包括窗函數(shù)法、頻率采樣法、和等波紋最佳逼近法；第二類是最優(yōu)設(shè)計(jì)法。設(shè)FIRDF的單位脈沖響應(yīng)h(n)的長(zhǎng)度為N N，則其頻率響應(yīng)函 數(shù)為N二H (ej)二為 h(n)eTn(1-1)一般將H(ej)表示成如下形式：H(ej)二Hg( )e門)(1-2)式中，Hgj)是的實(shí)函數(shù)(可以去負(fù)值)。與前面的表示形式，即H (ejK) = H g伸)e曲相比，Hg(co)與國(guó)不同。日仲)與伸)不HgCJ為幅頻特性函數(shù)，稱*）為相頻特性函數(shù)。同。為了區(qū)別于幅頻響應(yīng)函數(shù)H(eH(e 切和相頻響應(yīng)函數(shù)：（），稱第一類線性相位FIRDF的相位特性函數(shù)是的嚴(yán)格線性函數(shù)： - - （

3、1-3）第二類線性相位FIRDF的相位特性函數(shù)如下：-0 - （1-4）式中，是常數(shù)，厲是起始相位。入在信號(hào)處理中很 有實(shí)用價(jià)值（如希伯爾特變換器），這是FIRDF除了線性相位濾 波外，還具有真正交變換作用。1.2 窗函數(shù)設(shè)計(jì)法：窗函數(shù)設(shè)計(jì)法的基本思想是用FIRDF逼近希望的濾波特性。設(shè)希望逼近的濾波器的頻率響應(yīng)為Hde，其單位脈沖響應(yīng)用hdn表示。為了設(shè)計(jì)簡(jiǎn)單方便，通常選擇Hdej-為具有片段常數(shù)特性的理想濾波器。因此hdn是無(wú)限長(zhǎng)非因果序列，不能直接作 為FIRDF的單位脈沖響應(yīng)。窗函數(shù)設(shè)計(jì)法就是截取hdn為有限長(zhǎng)的一段因果序列，并用合適的窗口函數(shù)進(jìn)行加權(quán)作為FIRDF的單位脈沖響應(yīng)h n

4、。常見的窗函數(shù)，可以分為以下主要類型,(1)冪窗-米用時(shí)間變量某種冪次的函數(shù)，如矩形、二角 形、梯形或其它時(shí)間(t)的高次幕；(2)三角函數(shù)窗-應(yīng)用三角函數(shù)，即正弦或余弦函數(shù)等組合 成復(fù)合函數(shù)，例如漢寧窗、海明窗等；(3)指數(shù)窗-采用指數(shù)時(shí)間函數(shù)，例如高斯窗等 其性能如表1-1所示：名稱濾波器過(guò)渡帶寬最小阻帶衰減名稱濾波器過(guò)渡帶寬最小阻帶衰減矩形1.8n/M21dBPARZENWIN6.6n/M56db巴特利特6.1n/M25dBFLATTOPWIN19.6n/M108db漢寧6.2n/M44dBGAUSSWIN5.8n/M60db漢明6.6n/M51dBBARTHANNWIN3.6n/M40

5、db布萊克曼11n/M 74dBBLACKMANHARRS6.1n/M109dbBOHMANWIIJ5.8n/M51.5dbCHEBWIN15.2n/M113dbNUTTALLWIN15.4n/M 108dbTUKE YWIN2.4n/M22db表1-1常見窗函數(shù)性能表用窗口設(shè)計(jì)法基本步驟如下:(1)構(gòu)造希望逼近的頻率響應(yīng)函數(shù)Hde。以低通線性相位FIRDF設(shè)計(jì)為例，一般選擇Hder為線性理想低通濾波器，即(2)求出hdn。對(duì)Hde進(jìn)行IFT得到(3)加窗得到FIRDF的單位脈沖響應(yīng)hn,(1-7)式中，wn稱為窗口函數(shù)，其長(zhǎng)度為N N。如果要求第一類線性相位FIRDF，貝卩要求h n關(guān)于N

6、1 /2點(diǎn)偶對(duì)稱。而hdn關(guān)于n =.點(diǎn)偶對(duì)稱，所，N -1 /2，同時(shí)要求w n關(guān)于N -1 /2點(diǎn)偶對(duì)稱1.3 漢寧窗：漢寧窗(Hanning Window)又稱升余弦窗，漢寧窗可以看作是3個(gè)矩形時(shí)間窗的頻譜之和，或者說(shuō)是3個(gè)sin t型函數(shù)之和，而括號(hào)中的兩項(xiàng)相對(duì)于第一個(gè)譜窗向左、右各移動(dòng)了n/T,從而使旁瓣互相抵消，消去高頻干擾和漏能?？梢钥?出，漢寧窗主瓣加寬并降低，e%,0c、0,0,叭 H(1-5)Hdejdndncn-?二n_(1-6)H Hde ej旁瓣則顯著減小，從減小泄漏觀點(diǎn)出發(fā)，漢寧窗優(yōu)于矩形窗.但漢寧窗主瓣加寬，相當(dāng)于分析帶寬加寬，頻率分辨力下降。Whng為漢寧窗的幅

7、度響應(yīng)函數(shù)。二、設(shè)計(jì)流程圖：本課程設(shè)計(jì)主要是對(duì)一段數(shù)據(jù)，加入噪聲后，用漢寧窗函數(shù)法設(shè)計(jì)出的FIR濾波器對(duì)加入噪聲后的數(shù)據(jù)信號(hào)進(jìn)行濾波去噪處 理，并且分析對(duì)比前后時(shí)域和頻域波形的程序設(shè)計(jì)。程序的設(shè)計(jì)流程圖如下圖2-1所示：0 0跡警 WcWc。世(1-8)根據(jù)傅里葉變換的線性性質(zhì)和調(diào)制定理得到W ej = FT WhnnWhnge二N二/2二0.5WRg，0.25WRg-0.25WRgN -1ge_N /2（1-9）當(dāng)N N 1 1時(shí)，N N -1-1 N N，則Whng 叫Fg.嘰2co - IN -1(1-10)開始圖2-1程序設(shè)計(jì)流程圖三、matlab 設(shè)計(jì)函數(shù)及結(jié)果：用漢寧窗設(shè)計(jì)的FIR

8、數(shù)字低通濾波器的程序(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,handle

9、s,.) 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% unrecog

10、nized 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

11、response to help hanning % Last Modified by GUIDE v2.5 29-Jun-201111:03:04% 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

12、 nargin & ischar(varargin1)gui_State.gui_Callback = str2func(varargin1); end if nargoutvarargout1:nargout = gui_mainfcn(gui_State, varargin:); elsegui_mainfcn(gui_State, varargin:);end% End initialization code - DO NOT EDIT% - Executes just before hanning is made visible.function hanning_Opening

13、Fcn(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 lin

14、e arguments to hanning (see VARARGIN)hj1=load( E:a.txt );xn=hj1;% Choose default command line output for hanning handles.output = hObject;% Update handles structure guidata(hObject, handles);% UIWAIT makes hanning wait for user response (see UIRESUME)% uiwait(handles.hanning_gui);% - Outputs from th

15、is function are returned to the command line. function varargout =hanning_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (seeVARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handle

16、s and user data (see GUIDATA)% Get default command line output from handles structure varargout1 = 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 handl

17、es 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

18、 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 ),

19、get(0, defaultUicontrolBackgroundColor )set(hObject, BackgroundColor , white);endfunction 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)% H

20、ints: 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

21、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, defaultUicontrolBackground

22、Color )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 futureversion of MATLAB % handles str

23、ucture with handles and user data (see GUIDATA)H=findobj( Tag , edt_wp );aaa=get(H, H=findobj( Tag , edt_ws );aaa=get(H, 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

24、, whole);H=(H(1:1:501);w=(w(1:1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag); pha=angle(H);yn=conv(xn,h);axes(handles.axes1);plot(h);grid;title( 實(shí)際單位沖擊響應(yīng)); axes(handles.axes2);plot(w/pi,db);grid;title(漢寧窗濾波器的幅頻特性);axes(handles.axes3);plot(w/pi,pha);grid;title(漢寧窗濾波器的相頻特性);axes(handles.axes4);plot(xn);grid;title(輸入信號(hào));axes(handles.axes5);plot(yn);grid;title(輸出信號(hào));% - Executes on button press in btn_zero.function btn_zero_Callback(hObject, eventdata, handles)% hObject handle to btn_zero (see GCBO)% eventdata reserved - to be defined in a