哈工大數(shù)字信號(hào)處理實(shí)驗(yàn)報(bào)告

1、Harbin Institute of Technology數(shù)字信號(hào)處理實(shí)驗(yàn)報(bào)告學(xué)生姓名： 江世凱學(xué)號(hào)： 1122110307班級(jí)： 1221103專業(yè)： 電子科學(xué)與技術(shù)任課教師： 李楊所 在 單 位： 電子工程系2014年11月 實(shí)驗(yàn)一、用FFT作譜分析一、實(shí)驗(yàn)?zāi)康?1) 進(jìn)一步加深DFT算法原理和基本性質(zhì)的理解(因?yàn)镕FT只是DFT的一種快速算法， 所以FFT的運(yùn)算結(jié)果必然滿足DFT的基本性質(zhì))。(2) 熟悉FFT算法原理和FFT子程序的應(yīng)用。(3) 學(xué)習(xí)用FFT對(duì)連續(xù)信號(hào)和時(shí)域離散信號(hào)進(jìn)行譜分析的方法，了解可能出現(xiàn)的分析誤差及其原因，以便在實(shí)際中正確應(yīng)用FFT。二、實(shí)驗(yàn)內(nèi)容(1) 編制信

2、號(hào)產(chǎn)生子程序， 產(chǎn)生以下典型信號(hào)供譜分析用： (2) 畫出1 中所給出的信號(hào)，并逐個(gè)進(jìn)行譜分析。 下面給出針對(duì)各信號(hào)的FFT變換區(qū)間N以及對(duì)連續(xù)信號(hào)x6(t)的采樣頻率fs， 供實(shí)驗(yàn)時(shí)參考。 x1(n), x2(n), x3(n), x4(n), x5(n): N=8, 16 x6(t): fs=64(Hz), N=16, 32, 64（n=0:1:69）(3) 令x(n)=x4(n)+x5(n)， 用FFT計(jì)算 8 點(diǎn)和 16 點(diǎn)離散傅里葉變換， X(k)=DFTx(n)(4) 令x(n)=x4(n)+jx5(n)， 重復(fù)(2)。三、程序框圖圖1.實(shí)驗(yàn)程序框圖四、實(shí)驗(yàn)過(guò)程(1) 復(fù)習(xí)DFT的

3、定義、 性質(zhì)和用DFT作譜分析的有關(guān)內(nèi)容。(2) 復(fù)習(xí)FFT算法原理與編程思想， 并對(duì)照DIT-FFT運(yùn)算流圖和程序框圖， 讀懂本實(shí)驗(yàn)提供的FFT子程序。(3) 編制信號(hào)產(chǎn)生子程序， 產(chǎn)生以下典型信號(hào)供譜分析用： (4) 編寫主程序。(5) 按實(shí)驗(yàn)內(nèi)容要求， 上機(jī)實(shí)驗(yàn)， 并寫出實(shí)驗(yàn)報(bào)告。五、實(shí)驗(yàn)結(jié)果及分析1.實(shí)驗(yàn)結(jié)果（1）對(duì)x1(n)進(jìn)行FFT變換（N=8和N=16） 圖2 x1(n)進(jìn)行FFT變換結(jié)果（2）對(duì)x2(n)進(jìn)行FFT變換（N=8和N=16） 圖3 x2(n)FFT變換結(jié)果（3）對(duì)x3(n)進(jìn)行FFT變換（N=8和N=16） 圖4 x3(n) FFT變換結(jié)果（4）對(duì)x4(n)進(jìn)行F

4、FT變換（N=8和N=16） 圖5 x4(n) FFT變換結(jié)果（5）對(duì)x5(n)進(jìn)行FFT變換（N=8和N=16） 圖6 x5(n) FFT變換結(jié)果（6）對(duì)x6(n)進(jìn)行FFT變換（N=16、N=32和N=64） 圖7 x6(n) FFT變換結(jié)果（7）對(duì)x(n)=x4(n)+x5(n)進(jìn)行FFT變換（N=8和N=16） 圖8 x4(n)+x5(n) FFT變換結(jié)果（8）對(duì)x(n)=x4(n)+jx5(n)進(jìn)行FFT變換（N=8和N=16） 圖9 x4(n)+jx5(n)FFT變換結(jié)果（9）GUI設(shè)計(jì)結(jié)果2.分析：(1) 在N=8時(shí)，x2(n)和x3(n)的幅頻特性會(huì)相同嗎? 為什么? N=16

5、呢?答：在N=8的時(shí)候，x3(n)只是x2(n)以它的長(zhǎng)度8為周期，將其延拓成周期序列然后加以移位，最后截取主值區(qū)間（n=0到8）的序列值，因此x3(n)是x2(n)進(jìn)行循環(huán)位移后的結(jié)果。由于序列的循環(huán)位移性質(zhì)，因此，循環(huán)位移只影響到DFT后的相頻特性，而不影響幅頻特性，因此x2(n)和x3(n)的幅頻特性會(huì)相同。若N=16，此時(shí)，x2(n)和x3(n)做DFT即為它們分別進(jìn)行末尾補(bǔ)零后再進(jìn)行的DFT，則此時(shí)兩個(gè)經(jīng)過(guò)補(bǔ)零以后的序列就不滿足循環(huán)位移的性質(zhì)，因此x2(n)和x3(n)的幅頻特性就會(huì)發(fā)生變化。(2) 如果周期信號(hào)的周期預(yù)先不知道， 如何用FFT進(jìn)行譜分析答：在用FFT對(duì)信號(hào)進(jìn)行頻譜分

6、析時(shí)，首先要對(duì)信號(hào)進(jìn)行采樣，使之變成離散信號(hào)，然后就可按照前面的方法用FFT對(duì)離散信號(hào)進(jìn)行頻譜分析。按照采樣定理，采樣頻率fs應(yīng)當(dāng)大于信號(hào)最高頻率的2倍。若預(yù)先不知道周期信號(hào)的周期，應(yīng)先適當(dāng)截取M點(diǎn)進(jìn)行FFT，再將截取的長(zhǎng)度擴(kuò)大1倍重新截取，比較二者結(jié)果，若二者的差別滿足分析誤差的要求，就可以近似得到該信號(hào)的頻譜，假若不滿足誤差要求則繼續(xù)加倍截取的長(zhǎng)度進(jìn)行FFT，直到結(jié)果滿足誤差要求為止。(3) 結(jié)合實(shí)驗(yàn)中所得給定典型序列幅頻特性曲線，與理論結(jié)果比較， 并分析說(shuō)明誤差產(chǎn)生的原因以及用FFT作譜分析時(shí)有關(guān)參數(shù)的選擇方法。答：1. 誤差分析：1）對(duì)于x1（n）理論FFT頻譜為一個(gè)抽樣信號(hào)，由圖2可

7、以看出，隨著采樣率的提高，得到的FFT頻譜分辨率就越高，當(dāng)N趨于無(wú)限時(shí)頻譜包絡(luò)接近理論的抽樣函數(shù)。 2）序列x2（n）理論FFT頻譜為一個(gè)抽樣函數(shù)平方的信號(hào)，由圖3看出，隨著采樣率的提高，得到的FFT頻譜分辨率就越高，當(dāng)N趨于無(wú)限時(shí)頻譜包絡(luò)接近理論的抽樣函數(shù)。 3）對(duì)于x3（n），由圖4看出，隨著采樣率的提高，得到的FFT頻譜分辨率就越高，但對(duì)于這個(gè)函數(shù)來(lái)說(shuō)，N仍然過(guò)小，因此幅頻特性曲線與理論結(jié)果有較大差距。 4）序列x4（n）的理論FFT抽樣頻譜為單位沖激函數(shù)，因此只要滿足抽樣定理，F(xiàn)FT都可以與理論圖形一樣的曲線。由圖5可以看出，當(dāng)N=8,16時(shí)，滿足抽樣定理，能夠得到與理論一致的曲線。

8、5）序列x5（n）的理論FFT抽樣頻譜為單位沖激函數(shù)，因此只要滿足抽樣定理，F(xiàn)FT都可以與理論圖形一樣的曲線。由圖6可知，當(dāng)N=8時(shí)，不滿足抽樣定理，因此產(chǎn)生了混疊失真，當(dāng)N=8時(shí)，滿足抽樣定理，因此可得到與理論曲線一致的圖形。 6）序列x6（n）的理論FFT抽樣頻譜為有三個(gè)不同頻率分量的單位沖激函數(shù)，因此只要滿足抽樣定理，F(xiàn)FT都可以與理論圖形一樣的曲線。當(dāng)N=16時(shí)，不滿足抽樣定理，因此產(chǎn)生了混疊失真，當(dāng)N=32,64時(shí)，滿足抽樣定理，因此可得到與理論曲線一致的圖形，如圖7所示。 7）函數(shù)x4(n)+x5(n) 理論FFT抽樣頻譜為有兩個(gè)不同頻率分量的單位沖激函數(shù)，因此只要滿足抽樣定理，F(xiàn)

9、FT都可以與理論圖形一樣的曲線。當(dāng)N=8時(shí)，不滿足抽樣定理，因此產(chǎn)生了混疊失真，當(dāng)N=16時(shí)，滿足抽樣定理，因此可得到與理論曲線一致的圖形，如圖8所示。 8）序列x4(n)+jx5(n) 理論FFT抽樣頻譜為有兩個(gè)不同頻率分量的單位沖激函數(shù)，因此只要滿足抽樣定理，F(xiàn)FT都可以與理論圖形一樣的曲線。如圖9所示，當(dāng)N=8時(shí)，不滿足抽樣定理，因此產(chǎn)生了混疊失真，當(dāng)N=16時(shí)，滿足抽樣定理，因此可得到與理論曲線一致的圖形。2. 參數(shù)選擇;對(duì)時(shí)間序列做FFT變換時(shí)，抽樣頻率要要一些，從而提高分辨率減小誤差，同時(shí)抽樣頻率的選取必須滿足抽樣定理才能得到與理論相符的曲線。 六、實(shí)驗(yàn)源程序1. 對(duì)x1(n)進(jìn)行

10、FFT變換（N=8和N=16）function output_args = Untitled1( input_args )%UNTITLED1 Summary of this function goes here% Detailed explanation goes hereclear all;N=4;x=1,1,1,1;n=0:N-1;subplot(3,1,1);stem(n,abs(x),'g','LineWidth',1.3);title('x1(n)時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2

11、);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'c','LineWidth',1.3);title('FFTx1(n) : N=8');N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'m','LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),

12、9;y','LineWidth',1.3);title('FFTx1(n) : N=16');2. 對(duì)x2(n)進(jìn)行FFT變換（N=8和N=16）function output_args = Untitled2( input_args )%UNTITLED2 Summary of this function goes here% Detailed explanation goes hereclear all;x=1,2,3,4,4,3,2,1;N=8;n=0:N-1;subplot(3,1,1);stem(n,abs(x),'k',

13、9;LineWidth',1.3);title('x2(n) 時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'c-');title('FFTx2(n) : N=8');N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'m&#

14、39;,'LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx2(n) : N=16');3. 對(duì)x3(n)進(jìn)行FFT變換（N=8和N=16）function output_args = Untitled3( input_args )%UNTITLED3 Summary of this function goes here% Detailed explanation goes hereclear all;x=4,3,2,1,1,2,3,4;N=8;n=0:N-1;sub

15、plot(3,1,1);stem(n,abs(x),'k','LineWidth',1.3);title('x3(n) 時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'c-');title('FFTx3(n) : N=8');N=16;y2=fft(x,N);n=0:N-1;subplo

16、t(3,1,3);stem(n,fftshift(abs(y2),'m','LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx3(n) : N=16');4.對(duì)x4(n)進(jìn)行FFT變換（N=8和N=16）function output_args = Untitled3( input_args )%UNTITLED3 Summary of this function goes here% Detailed explanation goes herecle

17、ar all;n=0:15;%讀入長(zhǎng)度x=cos(pi/4*n);subplot(3,1,1);stem(n,abs(x),'k','LineWidth',1.3);title('x4(n) 時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'c-');title('FFTx4(n) : N=8&#

18、39;);N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'m','LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx4(n) : N=16');5.對(duì)x5(n)進(jìn)行FFT變換（N=8和N=16）function output_args = Untitled3( input_args )%UNTITLED3 Summary of this function goes her

19、e% Detailed explanation goes hereclear all;n=0:15;%讀入長(zhǎng)度x=sin(pi/8*n);subplot(3,1,1);stem(n,abs(x),'k','LineWidth',1.3);title('x5(n) 時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'

20、c-');title('FFTx5(n) : N=8');N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'m','LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx5(n) : N=16');6.對(duì)x6(n)進(jìn)行FFT變換（N=16、N=32和N=64）function output_args = Untitled3( input_args )%U

21、NTITLED3 Summary of this function goes here% Detailed explanation goes hereclear all;n=0:64;%讀入長(zhǎng)度x=cos(pi*8/64*n)+cos(pi*16/64*n)+cos(pi*20/64*n);subplot(4,1,1);stem(n,abs(x),'k','LineWidth',1.3);%plot(n,abs(x),'b');title('x6(t)抽樣得x6(n)');N=16;y1=fft(x,N);n=0:N-1;subp

22、lot(4,1,2);stem(n,fftshift(abs(y1),'r','LineWidth',1.3);hold on;plot(n,fftshift(abs(y1),'y-');title('FFTx6(n) : N=16');N=32;y2=fft(x,N);n=0:N-1;subplot(4,1,3);stem(n,fftshift(abs(y2),'m','LineWidth',1.3);hold on;plot(n,fftshift(abs(y2),'c-');ti

23、tle('FFTx6(n) : N=32');N=64;y3=fft(x,N);n=0:N-1;subplot(4,1,4);stem(n,fftshift(abs(y3),'b','LineWidth',1.3);hold on;plot(n,fftshift(abs(y3),'g-');title('FFTx6(n) : N=64');7.對(duì)x(n)=x4(n)+x5(n)進(jìn)行FFT變換（N=8和N=16）function output_args = Untitled2( input_args )%UNTITL

24、ED2 Summary of this function goes here% Detailed explanation goes hereclear all;n=0:15x4=cos(pi/4*n);x5=sin(pi/8*n);x=x4+x5;subplot(3,1,1);stem(n,abs(x);hold on;plot(n,abs(x),'y-');title('cos(pi/4*n)+sin(pi/8*n)時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subplot(3,1,2);stem(n,fftshift(abs(y1),

25、9;m');hold on;plot(n,fftshift(abs(y1),'c-');title('FFTx4+x5 : N=8');N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'r');hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx4+x5 : N=16');8.對(duì)x(n)=x4(n)+jx5(n)進(jìn)行FFT變換（N=8和N=16）function output_arg

26、s = Untitled2( input_args )%UNTITLED2 Summary of this function goes here% Detailed explanation goes hereclear all;n=0:15x4=cos(pi/4*n);x5=j*sin(pi/8*n);x=x4+x5;subplot(3,1,1);stem(n,abs(x);hold on;plot(n,abs(x),'y-');title('cos(pi/4*n)+jsin(pi/8*n)時(shí)間序列');N=8;y1=fft(x,N);n=0:N-1;subpl

27、ot(3,1,2);stem(n,fftshift(abs(y1),'m');hold on;plot(n,fftshift(abs(y1),'c-');title('FFTx4+x5 : N=8');N=16;y2=fft(x,N);n=0:N-1;subplot(3,1,3);stem(n,fftshift(abs(y2),'r');hold on;plot(n,fftshift(abs(y2),'g-');title('FFTx4+x5 : N=16');9.GUI設(shè)計(jì)源程序function

28、varargout = untitled3(varargin)% UNTITLED3 M-file for untitled3.fig% UNTITLED3, by itself, creates a new UNTITLED3 or raises the existing% singleton*.% H = UNTITLED3 returns the handle to a new UNTITLED3 or the handle to% the existing singleton*.% UNTITLED3('CALLBACK',hObject,eventData,handl

29、es,.) calls the local% function named CALLBACK in UNTITLED3.M with the given input arguments.% UNTITLED3('Property','Value',.) creates a new UNTITLED3 or raises the% existing singleton*. Starting from the left, property value pairs are% applied to the GUI before untitled3_OpeningFunc

30、tion gets called. An% unrecognized property name or invalid value makes property application% stop. All inputs are passed to untitled3_OpeningFcn via varargin.% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one% instance to run (singleton)".% See also: GUIDE, GUIDATA,

31、 GUIHANDLES% Copyright 2002-2003 The MathWorks, Inc.% Edit the above text to modify the response to help untitled3% Last Modified by GUIDE v2.5 23-Nov-2014 11:53:18% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, . 'gui_Singleton',

32、gui_Singleton, . 'gui_OpeningFcn', untitled3_OpeningFcn, . 'gui_OutputFcn', untitled3_OutputFcn, . 'gui_LayoutFcn', , . 'gui_Callback', );if nargin && ischar(varargin1) gui_State.gui_Callback = str2func(varargin1);endif nargout varargout1:nargout = gui_mainfcn

33、(gui_State, varargin:);else gui_mainfcn(gui_State, varargin:);end% End initialization code - DO NOT EDIT% - Executes just before untitled3 is made visible.function untitled3_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject handle to figure%

34、 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 untitled3 (see VARARGIN)% Choose default command line output for untitled3handles.output = hObject;% Update handles structureguidata(hObje

35、ct, handles);% UIWAIT makes untitled3 wait for user response (see UIRESUME)% uiwait(handles.figure1);% - Outputs from this function are returned to the command line.function varargout = untitled3_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);

36、% 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 editn_Callback(hObject, eventdata, handles)% hObject ha

37、ndle to editn (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 editn as text% str2double(get(hObject,'String') returns contents of editn as a doub

38、le% - Executes during object creation, after setting all properties.function editn_CreateFcn(hObject, eventdata, handles)% hObject handle to editn (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called% Hint

39、: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');endfunction editx_Callback(hObject, eventdata, handles)% hObje

40、ct handle to editx (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 editx as text% str2double(get(hObject,'String') returns contents of editx as a

41、 double% - Executes during object creation, after setting all properties.function editx_CreateFcn(hObject, eventdata, handles)% hObject handle to editx (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called%

42、 Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');endfunction editn1_Callback(hObject, eventdata, handles)%

43、 hObject handle to editn1 (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 editn1 as text% str2double(get(hObject,'String') returns contents of ed

44、itn1 as a double% - Executes during object creation, after setting all properties.function editn1_CreateFcn(hObject, eventdata, handles)% hObject handle to editn1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateF

45、cns called% Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');endfunction editn2_Callback(hObject, eventdata

46、, handles)% hObject handle to editn2 (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 editn2 as text% str2double(get(hObject,'String') returns con

47、tents of editn2 as a double% - Executes during object creation, after setting all properties.function editn2_CreateFcn(hObject, eventdata, handles)% hObject handle to editn2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after

48、all CreateFcns called% Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');end% - Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObject handle to pushbutton1 (see GCBO)% eventdata reserved - to be defined in a future version of MAT