fft频谱分析及应用

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1、实验二FFT频谱分析及应用四、验证实验1．用FFT进行典型信号的频谱分析①高斯序列：n=0:15;%定义序列的长度是15p=8;q=2;x=exp(-1*(n-p).^2/q);%利用fft函数实现富氏变换closeall;subplot(3,2,1);stem(x);subplot(3,2,2);stem(abs(fft(x)))p=8;q=4;x=exp(-1*(n-p).^2/q);%改变信号参数，重新计算subplot(3,2,3);stem(x);subplot(3,2,4);stem(abs(fft(x)))p=8;q=8;

2、x=exp(-1*(n-p).^2/q);subplot(3,2,5);stem(x);subplot(3,2,6);stem(abs(fft(x)))②衰减正弦序列%FFT进行衰减正弦序列的频谱分析n=0:30;%定义序列的长度是30a=0.1;f=0.0625;x=exp(-a*n).*sin(2*pi*f*n);closeall;subplot(2,1,1);stem(x);subplot(2,1,2);stem(abs(fft(x)))2．用FFT进行振幅光栅的衍射特性分析closeallclearall%theprogrameis

3、todemonstratedtheFFTofsquarefunctiont=-10*pi:0.1:10*pi;x=square(t/2,4);x=0.5+0.5*x;figure,plot(t,x)axis([-10*pi,10*pi,-0.51.5])%%%%%%%%%%%%%%%%%%%y=fft(x,1000000);y=abs(y);figure,plot(y(1:90000))%%%%%%%%%%%%%d=a+b;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%N增加一倍closeallclearallt=-10*pi:

4、0.1:10*pi;x=square(t/1,4);x=0.5+0.5*x;figure,plot(t,x)axis([-10*pi,10*pi,-0.51.5])y=fft(x,1000000);y=abs(y);figure,plot(y(1:90000))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%d=3a;改变光栅参数a,closeallclearallt=-10*pi:0.1:10*pi;x=square(t/2,33.3);x=0.5+0.5*x;figure,plot(t,x)axis([-10*pi,10

5、*pi,-0.51.5])y=fft(x,1000000);y=abs(y);figure,plot(y(1:90000))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%改变频谱分辨率（FFT计算的点数）closeallclearallt=-10*pi:0.1:10*pi;x=square(t/2,33.3);x=0.5+0.5*x;figure,plot(t,x)axis([-10*pi,10*pi,-0.51.5])%y=fft(x,10000);%y=abs(y);%figure,%plot(y(1:900))y

6、=fft(x);y=abs(y);figure,plot(y)%%%%%%%%%%%%五、设计实验1．模拟信号，以进行采样，求：（1）N＝40点FFT的幅度频谱，从图中能否观察出信号的2个频谱分量?（2）提高采样点数，如N＝128，256，512，再求该信号的幅度频谱，此时幅度频谱发生了什么变化？信号的2个模拟频率和数字频率各为多少？FFT频谱分析结果与理论上是否一致？实验代码：clc;clearall;N=40;%N=128;%%%%%%对N的值进行改变%N=256;%N=512;n=0:N-1;t=0.01*n;x=2*sin(4*pi

7、*t)+5*cos(8*pi*t);x1=x(1:N);X1=fft(x1,2048);figure,subplot(211),plot(0:N-1,x1);xlabel('n');ylabel('x(n)');title('时域波形');grid;subplot(212),plot(abs(X1));xlabel('k');ylabel('

8、X(k)

9、');title('幅频特性');grid;set(gcf,'color','w');N=40N=128N=256N=512答：N＝40点FFT的幅度频谱，有信号的两个频谱分量，信号的幅度增

10、加。模拟频率为77kHz，1967kHz，数字信号为967680Hz。FFT频谱分析结果与理论上是一致的。2．有限长序列x(n)={2,1,0,1,3};h(n)={1,3,2,