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1、信号与系统实验报告一、实验内容1. 利用 MATLAB 产生下列连续信号并作图。（1）51),1(2)(ttutx程序：t=-1:0.02:5; x=(t-1)0); y=-2*x; plot(t,y); axis(-1,5,-3,3); title(111000401 阶跃函数 ); （2）300),32sin()(3 . 0ttetxtt=0:0.001:30; x=exp(-0.3*t)*sin(2*t/3); plot(t,x); （3）1.01.0,3000cos100cos)(ttttxt=-0.1:0.001:0.1; x=cos(100*t)+cos(3000*t); plot
2、(t,x); title(111000401x=cos(100*t)+cos(3000*t) 实验二周期信号的傅里叶级数展开一、实验内容1、计算以上所列的四个基本周期信号的傅里叶级数展开。2、在计算机屏幕上画出周期信号的时域波形。3、分别计算出 5、10、15 次谐波迭加的值。4、把各次谐波迭加的波形重叠画在周期信号的时域波形上。5、观察逼近情况。(1)矩形脉冲function squ_fourier_seq(n) E=1; T1=0.5; Fn=2000; t0=T1/2; T=2; t = -T/2:1/Fn:T/2; n=5; squ = E*(1+square(2*pi/T1*t)/2
3、; squ=cat(2,squ(T1/4*Fn:end),squ(1:T1/4*Fn-1); a0=E*t0/T1; N=1:n; COSIN=cos(2*pi/T1*N*t); AN=(2*E)*sin(N*pi*t0/T1)./(N*pi); AN_1=meshgrid(AN,ones(size(t); COSIN_1=AN_1.*COSIN; ft=a0+sum(COSIN_1); plot(t,squ,r); hold on plot(t,ft,b); grid on; legend(原始脉冲信号 ,傅里叶级数逼近 ); hold off title(矩形脉冲 5 次谐波 111000
4、401白明辉 ) function squ_fourier_seq(n) E=1; T1=0.5; Fn=2000; t0=T1/2; T=2; t = -T/2:1/Fn:T/2; n=10; squ = E*(1+square(2*pi/T1*t)/2; squ=cat(2,squ(T1/4*Fn:end),squ(1:T1/4*Fn-1); a0=E*t0/T1; N=1:n; COSIN=cos(2*pi/T1*N*t); AN=(2*E)*sin(N*pi*t0/T1)./(N*pi); AN_1=meshgrid(AN,ones(size(t); COSIN_1=AN_1.*COS
5、IN; ft=a0+sum(COSIN_1); plot(t,squ,r); hold on plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off title(矩形脉冲 10 次谐波 111000401白明辉 ) function squ_fourier_seq(n) E=1; T1=0.5; Fn=2000; t0=T1/2; T=2; t = -T/2:1/Fn:T/2; n=15; squ = E*(1+square(2*pi/T1*t)/2; squ=cat(2,squ(T1/4*Fn:end),squ(1:T1/4*Fn-1)
6、; a0=E*t0/T1; N=1:n; COSIN=cos(2*pi/T1*N*t); AN=(2*E)*sin(N*pi*t0/T1)./(N*pi); AN_1=meshgrid(AN,ones(size(t); COSIN_1=AN_1.*COSIN; ft=a0+sum(COSIN_1); plot(t,squ,r); hold on plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off （2）锯齿波function saw_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:
7、1/Fn:T/2; n=5; saw= E*(sawtooth(2*pi/T1*t)/2; saw=fliplr(saw); if mod(n,2)=0 a=-1; else a=1; end N=1:n; A=a*1./N; A=meshgrid(A,ones(size(t); ft=A.*sin(N*2*pi/T1*t); ft=E/pi*ft; ft=sum(ft); plot(t,saw,r); hold on; plot(t,ft,b); grid on legend(原始脉冲信号 ,傅里叶级数逼近 ); axis(-1,1,-0.6,0.6); hold off tltle( 周期
8、锯齿脉冲信号5 次 111000401 白明辉) function saw_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=10; saw= E*(sawtooth(2*pi/T1*t)/2; saw=fliplr(saw); if mod(n,2)=0 a=-1; else a=1; end N=1:n; A=a*1./N; A=meshgrid(A,ones(size(t); ft=A.*sin(N*2*pi/T1*t); ft=E/pi*ft; ft=-sum(ft); plot(t,saw,r); hold
9、on; plot(t,ft,b); grid on legend(原始脉冲信号,傅里叶级数逼近); axis(-1,1,-0.6,0.6); hold off title( 锯齿波 10 次谐波白明辉 ) function saw_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=15; saw= E*(sawtooth(2*pi/T1*t)/2; saw=fliplr(saw); if mod(n,2)=0 a=-1; else a=1; end N=1:n; A=a*1./N; A=meshgrid(A,ones(
10、size(t); ft=A.*sin(N*2*pi/T1*t); ft=E/pi*ft; ft=sum(ft); plot(t,saw,r); hold on; plot(t,ft,b); grid on legend(原始脉冲信号,傅里叶级数逼近); axis(-1,1,-0.6,0.6); hold off title( 周期锯齿波信号15 次 111000401 白明辉 ) （3）三角波function tri_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=5; a=tripuls(-T1/2:1/Fn:T1
11、/2,0.5); a1=a(1:end-1); tri=; for i=1:T/T1-1 tri=tri a1; end tri=tri a; tri=cat(2,tri(T1/2*Fn:end),tri(1:T1/2*Fn-1); ft=zeros(1,length(t); for i=1:2:n ft=ft+1/(i2)*cos(i*2*pi/T1*t); end ft=E/2+4*E/(pi2)*ft; plot(t,tri,r); hold on; plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off title( 周期三角脉冲
12、5 次 111000401 白明辉 ) function tri_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=14; a=tripuls(-T1/2:1/Fn:T1/2,0.5); a1=a(1:end-1); tri=; for i=1:T/T1-1 tri=tri a1; end tri=tri a; tri=cat(2,tri(T1/2*Fn:end),tri(1:T1/2*Fn-1); ft=zeros(1,length(t); for i=1:2:n ft=ft+1/(i2)*cos(i*2*pi/T1
13、*t); end ft=E/2+4*E/(pi2)*ft; plot(t,tri,r); hold on; plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off Title( 周期三角脉冲信号10 次 111000401 白明辉 ) function tri_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=15; a=tripuls(-T1/2:1/Fn:T1/2,0.5); a1=a(1:end-1); tri=; for i=1:T/T1-1 tri=tr
14、i a1; end tri=tri a; tri=cat(2,tri(T1/2*Fn:end),tri(1:T1/2*Fn-1); ft=zeros(1,length(t); for i=1:2:n ft=ft+1/(i2)*cos(i*2*pi/T1*t); end ft=E/2+4*E/(pi2)*ft; plot(t,tri,r); hold on; plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off （4）半波余弦function cos_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t
15、= -T/2:1/Fn:T/2; n=5; acos=cos(2*pi/T1*t); bcos=(acos0); acos=bcos.*acos; ft=zeros(1,length(t); for i=2:2:n ft=ft+1/(i2-1)*cos(i*pi/2)*cos(i*2*pi/T1*t); end ft=E/pi+E/2*cos(2*pi/T1*t)-2*E/pi*ft; plot(t,acos,r); hold on; plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off Title( 周期半波余弦信号5 次谐波 111
16、000401 白明辉 ) function cos_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=3; acos=cos(2*pi/T1*t); bcos=(acos0); acos=bcos.*acos; ft=zeros(1,length(t); for i=2:2:n ft=ft+1/(i2-1)*cos(i*pi/2)*cos(i*2*pi/T1*t); end ft=E/pi+E/2*cos(2*pi/T1*t)-2*E/pi*ft; plot(t,acos,r); hold on; plot(t,ft,
17、b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off Title( 周期半波余弦信号10 次谐波 111000401 白明辉 ) function cos_fourier_seq(n) E=1; T1=0.5; Fn=2000; T=2; t = -T/2:1/Fn:T/2; n=15; acos=cos(2*pi/T1*t); bcos=(acos0); acos=bcos.*acos; ft=zeros(1,length(t); for i=2:2:n ft=ft+1/(i2-1)*cos(i*pi/2)*cos(i*2*pi/T1*t); end f
18、t=E/pi+E/2*cos(2*pi/T1*t)-2*E/pi*ft; plot(t,acos,r); hold on; plot(t,ft,b); grid on; legend(原始脉冲信号,傅里叶级数逼近); hold off Title( 周期半波余弦信号15 次谐波111000401 白明辉 ) 实验三离散信号的运算一、实验内容2. 利用 MATLAB 产生下列离散序列并作图。（1）, 055, 1)(nnx1515nk=-14:15; x=zeros(1,9),ones(1,11),zeros(1,10); stem(k,x); title(x(n)=1,-5=n=5 11100
19、0401白明辉 ); axis(-15,15,-0.5,1.5); （2）)25.0cos()25.0sin()9.0()(nnnxn，2020nk=-19:20; x3= (0.9).k; omega=pi/4; x1=sin(omega*k); x2=sin(omega*k+2* omega); x=(x1+x2).*x3; stem(k,x); title( x(n)=(0.9).n*sin(0.25*pi*n)+cos(0.25*pi*n) 111000401白明辉 ) 3. 已知序列：2, 3, 1,0,2, 1)(nx， 1 , 1, 1)(nh，计算离散卷积)()()(nhnxny，并绘出其波形。x=1,2,0,-1,3,2; h=1,-1,1; y=conv(x,h); subplot(2,1,1); stem(-2:length(y)-3,y); title(yk111000401 白明辉 );xlabel(k);