1、開(kāi)課學(xué)期2016-2017學(xué)年第2學(xué)期xlalbsjjAtaaaadXLxtea4占口wjiaaj-luaaaS44&口<jiaaj-luaaa4&口*ji-aaj-luaaa4&a金jiaaj-lbaaa4&口tjiaaj-lbaaa44u口wjiaaj-lbaaaua實(shí)驗(yàn)課程j信號(hào)與系統(tǒng)仿真實(shí)驗(yàn)實(shí)驗(yàn)項(xiàng)目一常用.號(hào)的頻譜分析及時(shí)域采樣定理*bAfaHaT-&B9i-iaaa*b8AbHa=W»11aHaaaa«iS.AaaaoSabaaaa«iaaaoSabapaaOSawaaaBaaaa*faawaaaa&

2、aaa"''a«aaaB3&aaa"''a«萩d，班級(jí)學(xué)號(hào)ij學(xué)生姓名Iiii-rvimn"va-Ha-Ha-H>"n>"n9"tbwr1.vrv.a-TBwr1.vrvr實(shí)驗(yàn)時(shí)間ii實(shí)驗(yàn)臺(tái)號(hào)iaiiiiiji_i操作成績(jī)I1報(bào)告成績(jī)|iii一、實(shí)驗(yàn)?zāi)康? .掌握常用信號(hào)的頻域分析方法；2 .掌握時(shí)域采樣定理；3 .掌握時(shí)域采樣信號(hào)恢復(fù)為原來(lái)連續(xù)信號(hào)的方法及過(guò)程。二、實(shí)驗(yàn)性質(zhì)驗(yàn)證性三、預(yù)習(xí)內(nèi)容1 .時(shí)域采樣定理的內(nèi)容及信號(hào)時(shí)域采樣過(guò)程；2 .連續(xù)信號(hào)經(jīng)時(shí)域采樣后，

3、信號(hào)的頻譜發(fā)生的變化；3 .時(shí)域采樣信號(hào)恢復(fù)為原來(lái)連續(xù)信號(hào)的方法及過(guò)程。四、實(shí)驗(yàn)內(nèi)容(編寫程序，繪制實(shí)驗(yàn)結(jié)果)1 .實(shí)現(xiàn)周期信號(hào)的頻譜f(t)=sin(2*80t)程序：fa='sin(2.*pi.*80.*t)'%原信號(hào)fs0=10000;%采樣頻率tp=0.1;%時(shí)間范圍t=-tp:1/fs0:tp;%信號(hào)持續(xù)時(shí)間范圍k1=0:999;k2=-999:-1;m1=length(k1);m2=length(k2);f=fs0*k2/m2,fs0*k1/m1;%信號(hào)頻率范圍w=-2*pi*k2/m2,2*pi*k1/m1;fx1=eval(fa);%把文本fa賦值給信號(hào)fx1F

4、X1=fx1*exp(-j*1:length(fx1)'*w);%進(jìn)行傅立葉變換figuresubplot(2,1,1),plot(t,fx1,'r');title('原信號(hào)');xlabel('時(shí)間t(s)');%原信號(hào)的時(shí)域波形圖axis(min(t),max(t),min(fx1),max(fx1);subplot(212),plot(f,abs(FX1),'r');title('原信號(hào)頻譜');xlabel('頻率f(Hz)');%頻域波形圖axis(-100,100,0,max(a

5、bs(FX1)+5);時(shí)間電原信號(hào)頻譜頻率陽(yáng)工)2 .實(shí)現(xiàn)非周期信號(hào)的頻譜，要求記錄結(jié)果并對(duì)結(jié)果進(jìn)行分析討論.(1)門函數(shù)信號(hào)g(t)的頻譜分析,(2)尺度變換之后門函數(shù)g(at)的頻譜分析.程序:令tao=1symstx=heaviside(t+0.5)-heaviside(t-0.5);F=fourier(x);subplot(211);ezplot(x,-2,2);subplot(212);ezplot(F,-10,10);heavisideft+1-heavisIde(1*10IIIIIRI1 -一0.5.0IlII.II-2-15-1-0.5DD511.52程序：令tao=1,a=4

6、symstx=heaviside(t+(1/8)-heaviside(t-(1/8);F=fourier(x);subplot(211);ezplot(x,-2,2);axis(-2,2,-1,2)subplot(212);ezplot(F);axis(-5,5,-0.5,0.5);(CQ5加間i+sln(w/8)/w-(cos(w/B)i-sin(w/B)/w口.510-1-0.5111111111-£-4-3-2-101234£w分析：經(jīng)過(guò)尺度變換，門函數(shù)的時(shí)間常數(shù)tao改變了，tao從1變成了1/4,門函數(shù)的幅度保持不變，但頻譜變化幅度比尺度變換前緩慢，頻譜的基波分量

7、降低了3.時(shí)域采樣及其恢復(fù)運(yùn)行給定實(shí)驗(yàn)程序，繪制運(yùn)行實(shí)驗(yàn)結(jié)果，總結(jié)實(shí)驗(yàn)結(jié)果，說(shuō)明采樣過(guò)程及恢復(fù)原信號(hào)的原理。程序：symstwf;%定義符號(hào)變量f=(1-2*abs(t)*exp(-j*w*t);%計(jì)算被積函數(shù)F=int(f,t,-1/2,1/2);%計(jì)算傅里葉系數(shù)F(w)F=simple(F);F%化簡(jiǎn)subplot(3,1,1),%繪制三角波的幅頻特性曲線F(w)low=-26*pi;high=-low;%設(shè)置w的上界和下界ezplot(abs(F),low:0.01:high);axis(lowhigh-0.10.5);xlabel('');title('三角波的

8、頻譜');subplot(3,1,2),%繪制經(jīng)過(guò)截止頻率為4*pi低通濾波器后的頻譜Y1(w)ezplot(abs(F),-4*pi:0.01:4*pi);axis(lowhigh-0.10.5);title('低通濾波后的頻譜');%采樣信號(hào)的頻譜是原信號(hào)頻譜的周期延拓，延拓周期為(2*pi)/Ts%PJ用頻移特性Ff(t)*exp(-j*w0*t)=F(w+w0)來(lái)實(shí)現(xiàn)subplot(3,1,3);法制采樣后的頻譜Y(w)Ts=0.2;%采樣信號(hào)的周期w0=(2*pi)/Ts;%S拓周期10*pifork=-2:2ft=f*exp(-j*w0*k*t);FT=in

9、t(ft,t,-1/2,1/2);ezplot(1/Ts)*abs(FT),(-4*pi-k*w0):0.01:(4*pi-k*w0);holdonendaxis(lowhigh-0.12.5);xlabel('');title('采樣后的頻譜');F=(8*sin(w/4)A2)/wA2三角波的撕詣0.40.2-60-6040-20020406030即采樣后的頻詣clc;closeall;%原信號(hào)fa='sin(2.*pi.*60.*t)'%原信號(hào)fs0=10000;%采樣頻率tp=0.1;%時(shí)間范圍t=-tp:1/fs0:tp;%信號(hào)持續(xù)時(shí)間

10、范圍k1=0:999;k2=-999:-1;m1=length(k1);m2=length(k2);f=fs0*k2/m2,fs0*k1/m1;%信號(hào)頻率范圍w=-2*pi*k2/m2,2*pi*k1/m1;fx1=eval(fa);%把文本fa賦值給信號(hào)fx1FX1=fx1*exp(-j*1:length(fx1)'*w);%進(jìn)行傅立葉變換figuresubplot(3,2,1),plot(t,fx1,'r');title('原信號(hào)');xlabel('時(shí)間t(s)');%原信號(hào)的時(shí)域波形圖axis(min(t),max(t),min(

11、fx1),max(fx1);subplot(322),plot(f,abs(FX1),'r');title('原信號(hào)頻譜');xlabel('頻率f(Hz)');%頻域波形圖axis(-100,100,0,max(abs(FX1)+5);%采樣信號(hào)fs=200;%采樣頻率，當(dāng)采樣頻率分別取80,150,200時(shí)，注意采樣信號(hào)的區(qū)別Ts=1/fs;%采樣周期t1=-tp:Ts:tp;%采樣信號(hào)橫坐標(biāo)范圍f1=fs*k2/m2,fs*k1/m1;%頻率范圍fb='sin(2.*pi.*60.*t1)'%待采樣信號(hào)fz=eval(fb)

12、;%引入信號(hào)FZ=fz*exp(-j*1:length(fz)'*w);%傅立葉變換subplot(323),stem(t1,fz,'.');%采樣信號(hào)的時(shí)域波形圖title('采樣信號(hào)');xlabel('時(shí)間t(s)');axis(min(t1),max(t1),min(fz),max(fz);subplot(324),plot(f1,abs(FZ),'r');%采樣信號(hào)的頻域波形圖title('采樣信號(hào)頻譜);xlabel('頻率f(Hz)');axis(-100,100,0,max(abs(

13、FZ)+5);%采樣信號(hào)的恢復(fù)T=1/fs;dt=T/10;tp=0.1;%采樣周期、時(shí)間問(wèn)隔、時(shí)間范圍賦值t=-tp:dt:tp;%時(shí)間范圍n=-tp/T:tp/T;TMN=ones(length(n),1)*t-n'*T*ones(1,length(t);%t-nTfh=fz*sinc(fs*TMN);%由取樣信號(hào)恢復(fù)信號(hào)k1=0:999;k2=-999:-1;m1=length(k1);m2=length(k2);w=-2*pi*k2/m2,2*pi*k1/m1;%頻率變量FH=fh*exp(-j*1:length(fh)'*w);%傅立葉變換subplot(325),p

14、lot(t,fh,'g');%恢復(fù)后的時(shí)域波形圖st1=sprintf('由取樣頻率fs=%d',fs);%標(biāo)注采樣頻率st2='恢復(fù)后的信號(hào)'st=st1,st2,title(st),xlabel('時(shí)間t(s)');axis(min(t),max(t),min(fh),max(fh);line(min(t),max(t),0,0);f=10*fs*k2/m2,10*fs*k1/m1;%頻率范圍subplot(326),plot(f,abs(FH),'g');%恢復(fù)后的頻域波形圖title('恢復(fù)后信號(hào)的頻譜'),xlabel('頻率f(Hz)');axis(-100,100,0,max(abs(FH)+5);1DOO原信號(hào)踴譜5000-100-50050100頻率中力采樣信號(hào)頻譜時(shí)間3)20W-10050050100頻率咐w)恢復(fù)后信號(hào)的頻譜由取樣頻率f/200恢復(fù)后的信號(hào)200100時(shí)間t-100-50050100頻率總結(jié)：采樣信號(hào)在一定條件下可以恢復(fù)為原來(lái)