离散傅里叶变换应用举例

x=[1,1,1,1];w=[0:1:500]*2*pi/500;

[H]=freqz(x,1,w);

magH=abs(H);phaH=angle(H);

subplot(2,1,1);plot(w/pi,magH);grid;xlabel('');ylabel('|X|'); title('DTFT的幅度')

subplot(2,1,2);plot(w/pi,phaH/pi*180);grid;

xlabel('以pi为单位的频率');label('度');

title('DTFT的相角')

N=4;w1=2*pi/N;k=0:N-1;

X=fft(x,N);

magX=abs(X);phaX=angle(X)*180/pi;

subplot(2,1,1);plot(w*N/(2*pi),magH,'--');axis([-0.1,4.1,0,5]);hold on; stem(k,magX);ylabel('|X(k)|');title('DFT的幅度:N=4');text(4.3,-1,'k'); hold off;

subplot(2,1,2);plot(w*N/(2*pi),phaH*180/pi,'--');axis([-0.1,4.1,-200,200]); hold on;

stem(k,phaX);ylabel('度');title('DFT的相角:N=4');text(4.3,-200,'k')

n=(0:1:9);x=cos(0.48*pi*n)+cos(0.52*pi*n);

w=[0:1:500]*2*pi/500;

X=x*exp(-1i*n'*w);

magx=abs(X);

x1=fft(x);magx1=abs(x1(1:1:10));

k1=0:1:9;w1=2*pi/10*k1;

subplot(3,1,1);stem(n,x);title('signalx(n),0<=n<=9');

axis([0,10,-2.5,2.5]);line([0,10],[0,0]);

subplot(3,1,2);plot(w/pi,magx);title('DTFT幅度');xlabel('w');axis([0,1,0,10]); subplot(3,1,3);stem(w1/pi,magx1);title('DFT幅度');

xlabel('频率（单位：pi)');axis([0,1,0,10])

实验总结：补零运算提供了一个较密的频谱和较好的图示形式，但因为在信号中只是附加了零，而没有增加任何新的信息，因此不能提供高分辨率的频谱。

n=(0:1:9);x=cos(0.48*pi*n)+cos(0.52*pi*n);

w=(0:1:500)*2*pi/500; %0-2*pi区域分为501点

X=x*exp(-1i*n'*w); %内部的矩阵维数必须一致

magx=abs(X);

x1=fft(x);magx1=abs(x1(1:1:10));

k1=0:1:9;w1=2*pi/10*k1;

subplot(3,1,1);stem(n,x);title('signalx(n),0<=n<=9');

axis([0,10,-2.5,2.5]); % axis([xmin xmax ymin ymax])

line([0,10],[0,0]);

subplot(3,1,2);plot(w/pi,magx);title('DTFT幅度');xlabel('w');axis([0,1,0,10]); subplot(3,1,3);stem(w1/pi,magx1);title('DTFT幅度');

xlabel('频率（单位：pi)');axis([0,1,0,10])

n=[0:1:9]; y=cos(0.48*pi*n)+cos(0.52*pi*n);

n1=[0:1:99]; x=[y(1:1:10),zeros(1,90)];

subplot(3,1,1);

stem(n1,x);

title('x(n) (0<=n<=9+90zeros'); xlabel('n');

axis([0,100,-2.5,2.5]); % axis([xmin xmax ymin ymax]) line([0,100],[0,0]);

w=[0:1:500]*2*pi/500; %0-2*pi区域分为501点

x1=fft(x);magx1=abs(x1(1:1:51));

x=x*exp(-j*n1'*w); magx=abs(x);

k1=[0:1:50]; w1=2*pi/100*k1;

subplot(3,1,2); plot(w/pi,magx); title('DTFT'); xlabel('w');

axis([0,1,0,10]); subplot(3,1,3);stem(w1/pi,magx1);

title('X(K)');xlabel('frequency in pi units'); axis([0,1,0,10]);

题目7-5.3、

n=[0:1:99];x=cos(0.48*pi*n)+cos(0.52*pi*n);

subplot(3,1,1);

stem(n,x);title('x(n) (0<=n<=99'); xlabel('n');

axis([0,100,-2.5,2.5]); %axis([xmin xmax ymin ymax]) line([0,100],[0,0]);

w=[0:1:500]*2*pi/500; %0-2*pi区域分为501点

x1=fft(x); magx1=abs(x1(1:1:50));

x=x*exp(-j*n'*w); magx=abs(x);

k1=0:1:49; w1=2*pi/100*k1;

subplot(3,1,2); plot(w/pi,magx); title('DTFT'); xlabel('w');

axis([0,1,0,55]); subplot(3,1,3); stem(w1/pi,magx1);

title('X(K)'); xlabel('frequency in pi units'); axis([0,1,0,55]);