Matab离散傅里叶变换试验报告

1、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）实验三 离散傅立叶变换（ DFT）1. 离散傅立叶级数给定有限长序列 1 2 3 4，延拓为周期 N=6 的周期序列，并求其 DFS。 代码：N1=6;x1=1 2 3 4; N2=length(x2); n1=0:5*N2-1; x2=x1,zeros(1,(6-length(x1);k=0:5*N2-1;x3=x2(mod(n1,N2)+1) Xk=x3*exp(-j*2*pi/N1).(n1*k);subplot(321),stem(x1,.);

2、title(原序列 )subplot(322),stem(x3,.);title(原序列周期延拓 )subplot(312),stem(Xk,.);title(DFS) subplot(325),stem(abs(Xk),.);title(DFS模值 )subplot(326),stem(angle(Xk),.);title(DFS相位 )结果：2. 求以下序列的 N=16,32,64 点的快速傅立叶变换x(n)=exp(-i*pi/8*n);x2(n)=cos(pi/8*n);x3(n)=sin(pi/8*n)(1) 代码：Fs=20;N1=16;n1=0:N1-1;xn1=exp(-i*p

3、i/8*n1);D1=2*pi*Fs/N1;N2=32;n2=0:N2-1;xn2=exp(-i*pi/8*n2);D2=2*pi*Fs/N2;N3=64;n3=0:N3-1;xn3=exp(-i*pi/8*n3);D3=2*pi*Fs/N3; k1=floor(-(N1-1)/2:(N1-1)/2);k2=floor(-(N2-1)/2:(N2-1)/2); k3=floor(-(N3-1)/2:(N3-1)/2);X1=fft(xn1,N1);X2=fft(xn2,N2);X3=fft(xn3,N3); subplot(3,4,1);stem(n1,xn1);title( 原信号 );yl

4、abel(C=16) subplot(3,4,2);stem(X1,.);title(FFT 结果 X); subplot(3,4,3);stem(k1*D1,abs(X1);title(X的模值 );subplot(3,4,4);plot(k1*D1,angle(X1);title(X 的相位 ); subplot(3,4,5);stem(n2,xn2);ylabel(C=32) subplot(3,4,6);stem(X2,.);subplot(3,4,7);stem(k2*D2,abs(X2); subplot(3,4,8);plot(k2*D2,angle(X2);subplot(3,

5、4,9);stem(n3,xn3);ylabel(C=64) subplot(3,4,10);stem(X3,.); subplot(3,4,11);stem(k3*D3,abs(X3); subplot(3,4,12);plot(k3*D3,angle(X3); 结果：(2) 代码：Fs=20;N1=16;n1=0:N1-1;xn1=cos(pi/8*n1);D1=2*pi*Fs/N1;N2=32;n2=0:N2-1;xn2=cos(pi/8*n2);D2=2*pi*Fs/N2;N3=64;n3=0:N3-1;xn3=cos(pi/8*n3);D3=2*pi*Fs/N3;k1=floor(-

6、(N1-1)/2:(N1-1)/2);k2=floor(-(N2-1)/2:(N2-1)/2); k3=floor(-(N3-1)/2:(N3-1)/2);X1=fft(xn1,N1);X2=fft(xn2,N2);X3=fft(xn3,N3);subplot(3,4,1);stem(xn1,.);title(axis(0,18,1.1*min(xn1),1.1*max(xn1);原信号 );ylabel(C=16);subplot(3,4,2);stem(X1,.);title(FFT结果 X);subplot(3,4,3);stem(abs(X1),.);title(X的模值 );axis

7、(0,18,1.1*min(abs(X1),1.1*max(abs(X1);的相位 );subplot(3,4,4);stem(angle(X1),.);title(X axis(0,18,1.1*min(angle(X1),1.1*max(angle(X1); subplot(3,4,5);stem(xn2,.);ylabel(C=32);axis(-2,35,1.1*min(xn2),1.1*max(xn2);subplot(3,4,6);stem(X2,.);subplot(3,4,7);stem(abs(X2),.);axis(0,35,1.1*min(abs(X2),1.1*max(

8、abs(X2);subplot(3,4,8);stem(angle(X2),.);axis(0,35,1.1*min(angle(X2),1.1*max(angle(X2);subplot(3,4,9);stem(xn3,.);ylabel(C=64);axis(-2,70,1.1*min(xn3),1.1*max(xn3);subplot(3,4,10);stem(X3,.);subplot(3,4,11);stem(abs(X3),.);axis(0,70,1.1*min(abs(X3),1.1*max(abs(X3);subplot(3,4,12);stem(angle(X3),.);a

9、xis(0,70,1.1*min(angle(X3),1.1*max(angle(X3); 结果：(3) 代码：Fs=20;N1=16;n1=0:N1-1;xn1=sin(pi/8*n1);D1=2*pi*Fs/N1;N2=32;n2=0:N2-1;xn2=sin(pi/8*n2);D2=2*pi*Fs/N2;N3=64;n3=0:N3-1;xn3=sin(pi/8*n3);D3=2*pi*Fs/N3;k1=floor(-(N1-1)/2:(N1-1)/2);k2=floor(-(N2-1)/2:(N2-1)/2);k3=floor(-(N3-1)/2:(N3-1)/2);X1=fft(xn1

10、,N1);X2=fft(xn2,N2);X3=fft(xn3,N3);subplot(3,4,1);stem(xn1,.);title(原信号 );ylabel(C=16)axis(0,18,1.1*min(xn1),1.1*max(xn1);subplot(3,4,2);stem(X1,.);title(FFT 结果 X);axis(0,18,-1.1*max(abs(X1),1.1*max(abs(X1);subplot(3,4,3);stem(abs(X1),.);的模值axis(0,18,1.1*min(abs(X1),1.1*max(abs(X1);title(X );subplot

11、(3,4,4);stem(angle(X1),.);axis(0,18,1.1*min(angle(X1),1.1*max(angle(X1);title(X 的 相位);subplot(3,4,5);stem(xn2,.);ylabel(C=32) axis(0,35,1.1*min(xn2),1.1*max(xn2);subplot(3,4,6);stem(X2,.);axis(0,35,-1.1*max(abs(X2),1.1*max(abs(X2);subplot(3,4,7);stem(abs(X2),.); axis(0,35,1.1*min(abs(X2),1.1*max(abs

12、(X2);subplot(3,4,8);stem(angle(X2),.); axis(0,35,1.1*min(angle(X2),1.1*max(angle(X2); subplot(3,4,9);stem(xn3,.);ylabel(C=64) axis(0,70,1.1*min(xn3),1.1*max(xn3);subplot(3,4,10);stem(X3,.);axis(0,70,-1.1*max(abs(X3),1.1*max(abs(X3);subplot(3,4,11);stem(abs(X3),.); axis(0,70,1.1*min(abs(X3),1.1*max(a

13、bs(X3);subplot(3,4,12);stem(angle(X3),.); axis(0,70,1.1*min(angle(X3),1.1*max(angle(X3);结果：3. 利用 DFT计算线性卷积； x1(n) 与给定序列 x1(n)=0.9n,n=0:11;h(n)=R 9(n) 求 x1(n)*h(n) h(n) 的 10 点圆周卷积。代码：n1=0:9;n2=0:11;m=0:N1-1;n=0:N1-1N=12;N1=10;x1=0.9.n2; x11=0.9.n1;x2=ones(1,9);x3=conv(x1,x2) x5=x11,zeros(1,N1-length(x11);x6=x2,zeros(1,N1-length(x2);H=zeros(N1,N1);x6=x6 zeros(1,N1-length(x6);for n=1:N1H(n,:)=x6(mod(n-m-1,N1)+1);endx4=x5*H;subplot(221),stem(x1,.);title(原序列 x1)axis(-1,14,0.6*min(x1),1.1*max(x1);subplot(