1、MAtlab傅里叶变换实验报告班级 信工082 学号 16 姓名 刘刚 实验组别 实验日期 室温 报告日期 成绩 报告内容：(目的和要求，原理，步骤，数据，计算，小结等)1.求信号的离散时间傅立叶变换并分析其周期性和对称性；给定正弦信号x(t)=2*cos(2*pi*10*t),fs=100HZ,求其DTFT。(a)代码：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(-
2、j).(t2*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(原信号x1);xlabel(t);ylabel(x1);subplot(2,2,3);stem(t2,x2);axis(0 1 1.1*min(x2) 1.1*max(x2);title(原信号采样结果x2);xlabel(t);ylabel(x2);subplot(2,2,2);stem(n,x5);axis(0 1 1.1*min(x5) 1.1*max(x5);xlabel
3、(n);ylabel(x2);title(采样函数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结果x4);（b）结果：2.用以下两个有限长序列来验证DTFT的线性、卷积和共轭特性；x1(n)=1 2 3 4 5 6 7 8 9 10 11 12;x2(n)=R10(n)(1) 线性:（a）代码：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=
4、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);%频率特性X3=x3*exp(-j*nx1*w);%频率特性X4=x4*exp(-j*nx1*w);%频率特性 subplot(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),ax
5、is(-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(w,angle(X1);ylabel(相位) subplot(5,3,10),plot(w,real(X1);ylabel(实部) subplot(5,3,13),plot(w,imag(X1); ylabel(虚部)subplot(5,3,5),plot(w,abs(X3); subplot(5,3,8),plot(w,angle(X3); subplot(5,3,11),plot(w,real(X
6、3);subplot(5,3,14),plot(w,imag(X3); subplot(5,3,6),plot(w,abs(X4); subplot(5,3,9),plot(w,angle(X4); subplot(5,3,12),plot(w,real(X4);subplot(5,3,15),plot(w,imag(X4); （b）结果：(2)卷积:（a）代码：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
7、;x3=conv(x1,x2);% x1卷积x2x4=x1*exp(-j*nx1*w);% x1频率特性x5=x2*exp(-j*nx2*w);% x2频率特性x6=x3*exp(-j*nx3*w);% x1卷积x2频率特性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卷积x2结果x3);figur
8、e,subplot(2,2,1),stem(x4,filled),title(x1的DTFT结果x4); subplot(2,2,2),stem(x5,filled),title(x2的DTFT结果x5); subplot(2,2,3),stem(x6,filled),title(x3的DTFT结果x6); subplot(2,2,4),stem(x7,filled),title(x4的DTFT结果x7); figure,subplot(3,2,1),stem(w,abs(x6), ylabel(幅度),title(x1卷积x2的DTFT); subplot(4,2,3),stem(w,ang
9、le(x6),ylabel(相位) subplot(4,2,5),stem(w,real(x6),ylabel(实部) subplot(4,2,7),stem(w,imag(x6),ylabel(虚部) subplot(4,2,2),stem(w,abs(x7), title(x1与x2的DTFT的乘积); subplot(4,2,4),stem(w,angle(x7); subplot(4,2,6),stem(w,real(x7); subplot(4,2,8),stem(w,imag(x7); （b）结果：(3)共轭:（a）代码：x1n=1 2 3 4 5 6 7 8 9 10 11 12
10、;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);stem(w,X1,.);title(x1n共轭的DTFT);subplot(212);stem(w,X2,.);title(x1n的DTFT取共轭且反折);（b）结果：3. 求LTI系统的频率响应给定系统H（Z）=B（Z）/A（Z），A=0.9877
11、7 -0.31183 0.0256B=0.98997 0.989 0.98997，求系统的幅频响应和相频响应。（要求使用filter(B,A,(n)求解。（a）结果：A=0.98777 -0.31183 0.0256;B=0.98997 0.989 0.98997;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
12、,.);title(幅频特性);xlabel(时间信号n);ylabel(信号幅度);subplot(2,2,3);stem(ph,.);title(相频特性);xlabel(时间信号n);ylabel(信号相位);（b）结果：4. 采样和频谱混叠给定信号x(t)=100*exp(-100*t)*cos(2*pi*500*t),求该信号的频谱；当采样频率分别为fs1=2000HZ,fs2=1000HZ;fs3=500HZ;fs4=200HZ，时输出序列的DTFT。（a）代码：x=100*exp(-100*t).*cos(2*pi*500*t);t=-2:0.1:2;w=-10:0.1:10;y
13、=x*(exp(-j).(t*w);subplot(2,1,1),plot(t,x);subplot(2,1,2),plot(w,y);title(原始信号的频谱);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);
14、title(经2000Hz采样后信号的DTFT);x2=100.*exp(-100*n2).*cos(2*pi*500*n2);y2=x2*(exp(-j).(n2*w);subplot(222);plot(w,y2);title(经1000Hz采样后信号的DTFT);x3=100.*exp(-100*n3).*cos(2*pi*500*n3); y3=x3*(exp(-j).(n3*w);subplot(223);plot(w,y3);title(经500Hz采样后信号的DTFT);x4=100.*exp(-100*n4).*cos(2*pi*500*n4);y4=x4*(exp(-j).(n4*w);subplot(224);plot(w,y4);title(经200Hz采样后信号的DTFT);（b）结果：
