MAtlab 傅里叶变换 实验报告文档格式.docx
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x5=[n>
=0.01];
x1=2*cos(2*f*pi*t1);
x2=2*cos(2*f*pi*t2);
x3=(exp(-j).^(t2'
*w));
x4=x2*x3;
subplot(2,2,1);
plot(t1,x1);
axis([011.1*min(x2)1.1*max(x2)]);
xlabel('
x(n)'
);
ylabel('
title('
原信号x1'
t'
x1'
subplot(2,2,3);
stem(t2,x2);
原信号采样结果x2'
x2'
subplot(2,2,2);
stem(n,x5);
axis([011.1*min(x5)1.1*max(x5)]);
n'
采样函数x2'
subplot(2,2,4);
stem(t2,x4);
axis([01-0.2+1.1*min(x4)1.1*max(x4)]);
x4'
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)=[123456789101112];
x2(n)=R10(n)
(1)线性:
w=linspace(-8,8,10000);
nx1=[0:
11];
nx2=[0:
9];
x1=[123456789101112];
x2=[1111111111];
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'
X4=x4*exp(-j*nx1'
%频率特性
subplot(5,3,1),stem(nx1,x1),axis([-1,13,0,15]);
),ylabel('
subplot(5,3,2),stem(nx2,x2),axis([-1,13,0,5]);
subplot(5,3,3),stem(nx1,x4),axis([-1,13,0,26]);
x4=2*x1+3*x3'
subplot(5,3,4),plot(w,abs(X1));
ylabel('
幅度'
)
subplot(5,3,7),plot(w,angle(X1));
相位'
subplot(5,3,10),plot(w,real(X1));
实部'
subplot(5,3,13),plot(w,imag(X1));
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(X3));
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));
(2)卷积:
nx1=0:
11;
nx2=0:
9;
nx3=0:
20;
w=linspace(-8,8,40);
%w=[-8,8]分10000份
x3=conv(x1,x2);
%x1卷积x2
x4=x1*exp(-j*nx1'
%x1频率特性
x5=x2*exp(-j*nx2'
%x2频率特性
x6=x3*exp(-j*nx3'
%x1卷积x2频率特性
x7=x4.*x5;
subplot(2,2,1),stem(nx1,x1),axis([-1,15,0,15]),title('
subplot(2,2,2),stem(nx2,x2),axis([-1,15,0,5]),title('
subplot(2,1,2),stem(nx3,x3),axis([-1,25,0,80]);
x1卷积x2结果x3'
figure,subplot(2,2,1),stem(x4,'
filled'
),title('
x1的DTFT结果x4'
subplot(2,2,2),stem(x5,'
x2的DTFT结果x5'
subplot(2,2,3),stem(x6,'
x3的DTFT结果x6'
subplot(2,2,4),stem(x7,'
x4的DTFT结果x7'
figure,subplot(3,2,1),stem(w,abs(x6)),ylabel('
x1卷积x2的DTFT'
subplot(4,2,3),stem(w,angle(x6)),ylabel('
subplot(4,2,5),stem(w,real(x6)),ylabel('
subplot(4,2,7),stem(w,imag(x6)),ylabel('
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));
(3)共轭:
x1n=[123456789101112];
N1=length(x1n);
n1=0:
N1-1;
x1=real(x1n);
x2=imag(x1n);
x2n=x1-j*x2;
X1=x2n*(exp(-j).^(n1'
X2=x1n*(exp(j).^(n1'
x3=real(X2);
x4=imag(X2);
X2=x3-j*x4;
figure,subplot(211);
stem(w,X1,'
.'
x1n共轭的DTFT'
subplot(212);
stem(w,X2,'
x1n的DTFT取共轭且反折'
3.求LTI系统的频率响应
给定系统H(Z)=B(Z)/A(Z),A=[0.98777-0.311830.0256]
B=[0.989970.9890.98997],求系统的幅频响应和相频响应。
(要求使用filter(B,A,δ(n))求解。
(a)结果:
A=[0.98777-0.311830.0256];
B=[0.989970.9890.98997];
C=[100000000000000000000000000]
y=filter(B,A,C);
stem(y,'
原始序列'
mag=abs(y);
ph=angle(y);
ph=ph*180/pi;
stem(mag,'
幅频特性'
时间信号n'
信号幅度'
stem(ph,'
相频特性'
信号相位'
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。
x=100*exp(-100*t).*cos(2*pi*500*t);
t=-2:
0.1:
2;
y=x*(exp(-j).^(t'
subplot(2,1,1),plot(t,x);
subplot(2,1,2),plot(w,y);
原始信号的频谱'
figure,fs1=2000;
Ts1=1/fs1;
n1=-2:
Ts1:
fs2=1000;
Ts2=1/fs2;
n2=-2:
Ts2:
fs3=500;
Ts3=1/fs3;
n3=-2:
Ts3:
fs4=200;
Ts4=1/fs4;
n4=-2:
Ts4:
x1=100.*exp(-100*n1).*cos(2*pi*500*n1);
y1=x1*(exp(-j).^(n1'
subplot(221);
plot(w,y1);
经2000Hz采样后信号的DTFT'
x2=100.*exp(-100*n2).*cos(2*pi*500*n2);
y2=x2*(exp(-j).^(n2'
subplot(222);
plot(w,y2);
经1000Hz采样后信号的DTFT'
x3=100.*exp(-100*n3).*cos(2*pi*500*n3);
y3=x3*(exp(-j).^(n3'
subplot(223);
plot(w,y3);
经500Hz采样后信号的DTFT'
x4=100.*exp(-100*n4).*cos(2*pi*500*n4);
y4=x4*(exp(-j).^(n4'
subplot(224);
plot(w,y4);
经200Hz采样后信号的DTFT'