MAtlab傅里葉變換實驗報告

1、班級 信工082 學號 16 姓名 劉剛 實驗組別 實驗日期 室溫 報告日期 成績 報告內(nèi)容：(目的和要求，原理，步驟，數(shù)據(jù)，計算，小結(jié)等)1.求信號的離散時間傅立葉變換并分析其周期性和對稱性；給定正弦信號x(t)=2*cos(2*pi*10*t),fs=100HZ,求其DTFT。(a)代碼：f=10;T=1/f;w=-10:0.2:10;t1=0:0.0001:1;t2=0:0.01:1;n1=-2;n2=8;n0=0;n=n1:0.01:n2;x5=n>=0.01;x1=2*cos(2*f*pi*t1);x2=2*cos(2*f*pi*t2);x3=(exp(-j).(t2'

2、*w);x4=x2*x3;subplot(2,2,1);plot(t1,x1);axis(0 1 1.1*min(x2) 1.1*max(x2);xlabel('x(n)');ylabel('x(n)');title('原信號x1');xlabel('t');ylabel('x1');subplot(2,2,3);stem(t2,x2);axis(0 1 1.1*min(x2) 1.1*max(x2);title('原信號采樣結(jié)果x2');xlabel('t');ylabel(

3、9;x2');subplot(2,2,2);stem(n,x5);axis(0 1 1.1*min(x5) 1.1*max(x5);xlabel('n');ylabel('x2');title('采樣函數(shù)x2');subplot(2,2,4);stem(t2,x4);axis(0 1 -0.2+1.1*min(x4) 1.1*max(x4);xlabel('t');ylabel('x4');title('DTFT結(jié)果x4');（b）結(jié)果：2.用以下兩個有限長序列來驗證DTFT的線性、卷積和共

4、軛特性；x1(n)=1 2 3 4 5 6 7 8 9 10 11 12;x2(n)=R10(n)(1) 線性:（a）代碼：w=linspace(-8,8,10000);nx1=0:11; nx2=0:9;x1=1 2 3 4 5 6 7 8 9 10 11 12;x2=1 1 1 1 1 1 1 1 1 1;x3=x2,zeros(1,(length(x1)-length(x2);x4=2*x1+3*x3;X1=x1*exp(-j*nx1'*w);%頻率特性X3=x3*exp(-j*nx1'*w);%頻率特性X4=x4*exp(-j*nx1'*w);%頻率特性 sub

5、plot(5,3,1),stem(nx1,x1),axis(-1,13,0,15);title('x1'), ylabel('x(n)'); subplot(5,3,2),stem(nx2,x2),axis(-1,13,0,5);title('x2'); subplot(5,3,3),stem(nx1,x4),axis(-1,13,0,26);title('x4=2*x1+3*x3'); subplot(5,3,4),plot(w,abs(X1); ylabel('幅度') subplot(5,3,7),plot(

6、w,angle(X1);ylabel('相位') subplot(5,3,10),plot(w,real(X1);ylabel('實部') subplot(5,3,13),plot(w,imag(X1); ylabel('虛部')subplot(5,3,5),plot(w,abs(X3); subplot(5,3,8),plot(w,angle(X3); subplot(5,3,11),plot(w,real(X3);subplot(5,3,14),plot(w,imag(X3); subplot(5,3,6),plot(w,abs(X4); s

7、ubplot(5,3,9),plot(w,angle(X4); subplot(5,3,12),plot(w,real(X4);subplot(5,3,15),plot(w,imag(X4); （b）結(jié)果：(2)卷積:（a）代碼：nx1=0:11; nx2=0:9; nx3=0:20; w=linspace(-8,8,40); %w=-8，8分10000份 x1=1 2 3 4 5 6 7 8 9 10 11 12;x2=1 1 1 1 1 1 1 1 1 1;x3=conv(x1,x2);% x1卷積x2x4=x1*exp(-j*nx1'*w);% x1頻率特性x5=x2*exp(-

8、j*nx2'*w);% x2頻率特性x6=x3*exp(-j*nx3'*w);% x1卷積x2頻率特性x7=x4.*x5; subplot(2,2,1),stem(nx1,x1),axis(-1,15,0,15),title('x1');subplot(2,2,2),stem(nx2,x2),axis(-1,15,0,5),title('x2');subplot(2,1,2),stem(nx3,x3),axis(-1,25,0,80);title('x1卷積x2結(jié)果x3');figure,subplot(2,2,1),stem(x

9、4,'filled'),title('x1的DTFT結(jié)果x4'); subplot(2,2,2),stem(x5,'filled'),title('x2的DTFT結(jié)果x5'); subplot(2,2,3),stem(x6,'filled'),title('x3的DTFT結(jié)果x6'); subplot(2,2,4),stem(x7,'filled'),title('x4的DTFT結(jié)果x7'); figure,subplot(3,2,1),stem(w,abs(x6),

10、 ylabel('幅度'),title('x1卷積x2的DTFT'); subplot(4,2,3),stem(w,angle(x6),ylabel('相位') subplot(4,2,5),stem(w,real(x6),ylabel('實部') subplot(4,2,7),stem(w,imag(x6),ylabel('虛部') subplot(4,2,2),stem(w,abs(x7), title('x1與x2的DTFT的乘積'); subplot(4,2,4),stem(w,angle(

11、x7); subplot(4,2,6),stem(w,real(x7); subplot(4,2,8),stem(w,imag(x7); （b）結(jié)果：(3)共軛:（a）代碼：x1n=1 2 3 4 5 6 7 8 9 10 11 12;w=-10:10;N1=length(x1n);n1=0:N1-1;x1=real(x1n);x2=imag(x1n);x2n=x1-j*x2; X1=x2n*(exp(-j).(n1'*w);X2=x1n*(exp(j).(n1'*w);x3=real(X2);x4=imag(X2);X2=x3-j*x4;figure,subplot(211)

12、;stem(w,X1,'.');title('x1n共軛的DTFT');subplot(212);stem(w,X2,'.');title('x1n的DTFT取共軛且反折');（b）結(jié)果：3. 求LTI系統(tǒng)的頻率響應給定系統(tǒng)H（Z）=B（Z）/A（Z），A=0.98777 -0.31183 0.0256B=0.98997 0.989 0.98997，求系統(tǒng)的幅頻響應和相頻響應。（要求使用filter(B,A,(n)求解。（a）結(jié)果：A=0.98777 -0.31183 0.0256;B=0.98997 0.989 0.98997;

13、C=1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0y=filter(B,A,C);subplot(2,2,1);stem(y,'.');title('原始序列');mag=abs(y);ph=angle(y);ph=ph*180/pi;subplot(2,2,2);stem(mag,'.');title('幅頻特性');xlabel('時間信號n');ylabel('信號幅度');subplot(2,2,3);stem(ph,'.&

14、#39;);title('相頻特性');xlabel('時間信號n');ylabel('信號相位');（b）結(jié)果：4. 采樣和頻譜混疊給定信號x(t)=100*exp(-100*t)*cos(2*pi*500*t),求該信號的頻譜；當采樣頻率分別為fs1=2000HZ,fs2=1000HZ;fs3=500HZ;fs4=200HZ，時輸出序列的DTFT。（a）代碼：x=100*exp(-100*t).*cos(2*pi*500*t);t=-2:0.1:2;w=-10:0.1:10;y=x*(exp(-j).(t'*w);subplot(2,

15、1,1),plot(t,x);subplot(2,1,2),plot(w,y);title('原始信號的頻譜');figure,fs1=2000;Ts1=1/fs1;n1=-2:Ts1:2; fs2=1000;Ts2=1/fs2;n2=-2:Ts2:2; fs3=500;Ts3=1/fs3;n3=-2:Ts3:2; fs4=200;Ts4=1/fs4;n4=-2:Ts4:2;x1=100.*exp(-100*n1).*cos(2*pi*500*n1);y1=x1*(exp(-j).(n1'*w);subplot(221);plot(w,y1);title('經(jīng)2000Hz采樣后信號的DTFT');x2=100.*exp(-100*n2).*cos(2*pi*500*n2);y2=x2*(exp(-j).(n2'*w);subplot(222);plot(w,y2);title('經(jīng)1000Hz采樣后信號的DTFT');x3=100.*exp(-100*n3).*cos(