信号的频谱分析

信号的频谱分析实习报告实验目的FFTCFS，CTFTDFT（FFT）的关系。FFT分析离散周期，非周期信号的频谱，如周期，非周期方波，正弦信号等。理解DFS，DTFTDFT（FFT）谱分析方法的异同。实验内容 FFT，分析并画出sin(100t),cos(100t断长度，分析混叠与泄漏对单一频率成分信号频谱的影响。 FFT间隔与截断长度，分析混叠与泄漏对信号频谱的影响。 利用FFT，分析并画出etu(t分析混叠与泄漏对信号频谱的影响。利用不同窗函数对内容3.中的信号进行加窗处理，分析对信号频谱的影响；*FFT计算线性卷积，验证‘实验三’中时域结果的正确性。具体实验步骤及实验结果1. sin(100t),cos(100t频谱a．sin(100πt)程序，图像、频谱分析图及其幅度相位图closeall;clc;clear;t=0:0.001:0.999;subplot(311)a=sin(100*pi*t);plot(t,a);gridon;title('sin100pi*t');xlabel('T');b=fft(a);subplot(312);stem(t*1000,abs(b)/1000,'fill');xlabel('Hz');gridon;title('频率特性')subplot(313)stem(t*1000,angle(b)/1000,'fill');xlabel('Hz');gridon;title('相频特性')sin100pi*t10-10.5

0 0.1 0.2 0.3 0.4 0.5T

0.6 0.7 0.8 0.9 100 x10-35

200 300 400 500Hz

600 700 800 900 10000-50 100 200 300 400 Hz

600 700 800 900 1000b．cos(100πt)程序，图像、频谱分析图及其幅度相位图closeall;clc;clear;t=0:0.001:0.999;subplot(311)a=cos(100*pi*t);plot(t,a);gridon;title('sin100pi*t');xlabel('T');b=fft(a);subplot(312);stem(t*1000,abs(b)/1000,'fill');xlabel('Hz');gridon;title('频率特性')subplot(313)stem(t*1000,angle(b)/1000,'fill');xlabel('Hz');gridon;title('相频特性')cos100pi*t10-10.5

0 0.1 0.2 0.3 0.4 0.5T

0.6 0.7 0.8 0.9 100 x10-35

200 300 400 500Hz

600 700 800 900 10000-50 100 200 300 400 Hz

600 700 800 900 1000c. 10Hz谱的影响。正确的正弦波特性曲线采样间隔为0.01采样个数10010-110.500.050-0.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 10 20 30 40 50 60 70 80 90 1000 10 20 30 40 50 60 70 80 90 100发生混叠现象采样间隔0.1510-10.10.05

0 5 10 1500x10-350

5000 10000 15000-50 5000 10000 15000发生泄漏现象采样间隔0.01采样个数11210-110.5050-5

0 0.2 0.4 0.6 0.8 1 1.2 1.40 20 40 60 80 100 1200 20 40 60 80 100 120 140clc;t=0:0.01:1-0.01a=square(2*pi*t,50)subplot(311)stem(t,a,'fill')b=fft(a)subplot(312)stem(t*100,abs(b)/100,'fill')gridonsubplot(313)stem(t*100,angle(b)/100,'fill')10-110.500.020-0.02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 10 20 30 40 50 60 70 80 90 1000 10 20 30 40 50 60 70 80 90 100混叠现象clc;t=0:0.01:1-0.01a=square(250*t,50)subplot(311)stem(t,a,'fill')b=fft(a)subplot(312)stem(t*100,abs(b)/100,'fill')subplot(313)stem(t*100,angle(b)/100,'fill')10-110-10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110.500.050-0.05

0 10 20 30 40 50 60 70 80 90 1000 10 20 30 40 50 60 70 80 90 100方波的泄露现象clc;t=0:0.01:0.86a=square(20*t,50)subplot(311)stem(t,a,'fill')b=fft(a)subplot(312)stem(t*86,abs(b)/86,'fill')gridonsubplot(313)stem(t*86,angle(b)/86,'fill')0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.910.500.050-0.05

0 10 20 30 40 50 60 70 80 900 10 20 30 40 50 60 70 80 90etu(t信号的频谱、真实值与理论值分析closeall;clc;clear;t=0:0.01:30-0.01;a=1+j*pi*2*t;a=1./a;subplot(311);plot(t,a);title('理论值');gridon;subplot(312);plot(t,a,'r');axis([0,15,0,1]);title('对比图');holdon;b=exp(-t);c=fft(b);plot(t,abs(c)/100,'g');gridon;holdon;subplot(313);stem(t,angle(c),'fill');title('相位图');gridon;理论值10.5010.5

0 5 10 15对比图

20 25 3000 5相位图20

10 15-20 5 10 15 20 25 303.a．加入矩形窗closeall;clc;clear;w=0:0.1:30-0.1;a=1+j*2*pi*w;a=1./a;plot(w,a,'r');holdon;t=0:0.1:30-0.1;b=exp(-t);c=fft(b);plot(t,c/10,'g');axis([0,15,0,1]);gridon;holdon;d=boxcar(600)';y=d(301:600);e=y.*b;f=fft(e);plot(t,f/10,'y');110.90.80.70.60.50.40.30.20.10051015hanningcloseall;clc;clear;w=0:0.1:30-0.1;a=1+j*2*pi*w;a=1./a;plot(w,a,'r');holdon;t=0:0.1:30-0.1;b=exp(-t);c=fft(b);plot(t,c/10,'g');axis([0,15,0,1])gridon;holdon;d=hanning(600)';y=d(301:600);e=b.*y;f=fft(e);plot(t,abs(f)/10,'b')0.90.80.70.60.50.40.30.20.10051015hammingcloseall;clc;clear;w=0:0.1:30-0.1;a=1+j*2*pi*w;a=1./a;plot(w,a,'r');holdon;t=0:0.1:30-0.1;b=exp(-t);c=fft(b);plot(t,c/10,'g');axis([0,15,0,1]);gridon;holdon;d=hamming(600)';y=d(301:600)e=y.*b;f=fft(e)plot(t,f/10,'b')0.90.80.70.60.50.40.30.20.10051015closeall;clc;clear;t=0:0.1:30-0.1;b=exp(-t);c=fft(b);plot(t,c/10,'g');axis([0,15,0,1]);gridon;holdon;d=boxcar(600)';y=d(301:600);e=y.*b;f=fft(e);plot(t,f/10,'y');gridon;holdon;d=hamming(600)';y=d(301:600);e=y.*b;f=fft(e);plot(t,f/10,'b');gridon;holdon;d=hanning(600)';y=d(301:600);e=b.*y;f=fft(e);plot(t,abs(f)/10,'r');;10.90.80.70.60.50.40.30.20.100 5 10 15*FFTcloseall;clc;clear;t=0:0.01:10-0.01;b=exp(-t);c=fft(b);subplot(221);stem(t,c/100,'g');axis([0,5,0,1]);w=boxcar(1000)';d=fft(w);subplot(222);stem(t,d/1000,'r');a=conv(d,c)/2/pim=length(a)-1n=0:1:m;subplot(223);stem(n,a/m/10,'fill');axis([0,15,0,1]);subplot(224);e=w.*b;plot(t,e,'r');holdon;plot(n,a/m/10,'b');axis([0,15,0,1]);g