信号与系统上机实验报告Word下载.docx
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信号与系统上机实验报告Word下载.docx
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clearall;
%计算信号值
n=[0:
31];
temp=pi*n/4;
x1=sin(temp).*cos(temp);
x2=cos(temp).^2;
%orx2=power(cos(temp),2);
%orx2=pow2(cos(temp));
x3=sin(temp).*cos(temp/2);
%绘图
subplot(3,1,1);
stem(x1);
title('
x1[n]T=4'
);
xlabel('
n'
subplot(3,1,2);
stem(x2);
x2[n]T=4'
);
subplot(3,1,3);
stem(x3);
x3[n]T=16'
(c)Result
(d)Conclusion
Thefirstsignal’sfundamentalperiodis4.
Andsecondsignal’sfundamentalperiodis4
Thethirdsignal’sfundamentalperiodis16.
2.离散时间系统性质:
●1.4节(a)
x1=impseq(0,-1,10);
%x1=[0,1,zeros(1,10)];
x2=2*x1;
x=x1+x2;
y1=sin(pi/2*x1);
y2=sin(pi/2*x2);
y=sin(pi/2*x);
%绘图
subplot(2,1,1);
stem([-1:
10],y1+y2);
y1[n]+y2[n](Thesumofy1andy2wheninputisx1[n]andx2[n])'
subplot(2,1,2);
10],y);
Theoutputy[n]wheninputisx[n]=x1[n]+x2[n]'
补充:
function[x,n]=impseq(n0,n1,n2)
%generatex(n)=delata(n-n0);
n1<
=n<
=n2
%xisthesignal,nisthesequencenumber.
n=[n1:
n2];
x=[(n-n0)==0];
function[x,n]=stepseq(n0,n1,n2)
%generatex(n)=u(n-n0);
x=[(n-n0)>
=0];
●1.4节(b)
[x1,n1]=stepseq(0,-5,9);
%orn1=[-5:
9];
x1=[zeros(1,5),ones(1,10)];
[x2,n2]=stepseq(-1,-5,9);
%orn2=[-5:
x2=[zeros(1,4),ones(1,11)];
y=x1+x2;
stem(n1,x1);
Theinputx[n]=u[n]'
stem(n1,y);
Theoutputy[n]'
3.卷积计算:
●2.1节(c)
[x,n1]=stepseq(0,0,5);
%orn1=[0:
5];
x=[ones(1,6)];
h=[012345];
y=conv(x,h);
ny=[0:
10];
stem(n1,x);
inputx[n]'
stem(n1,h);
systemfunctionh[n]'
stem(ny,y);
outputy[n]withsequence'
4.函数Filter的使用:
●2.2节(c)(d);
a3=[1,-0.8];
b3=[0,2];
x=[1234];
y3=filter(b3,a3,x);
stem(y3);
5.函数Freqz的使用:
●3.2节(a,b,c);
a1=[1-0.8];
b1=[20-1];
N=4;
[h1omega1]=freqz(b1,a1,N);
%查看变量值
[h2omega2]=freqz(b1,a1,N,'
whole'
6.LTI系统的特征函数:
●3.4节(a)
%计算输入信号并画波形
n=[-20:
100];
x1=exp(j*n*pi/4);
x2=sin(pi*n/8+pi/16);
x3=power(0.9,n);
x4=n+1;
subplot(2,2,1);
plot(n,real(x1));
holdon;
plot(n,imag(x1),'
r'
realandimagepartofx1[n]'
subplot(2,2,2);
plot(n,x2);
x2[n]'
subplot(2,2,3);
plot(n,x3);
x3[n]'
subplot(2,2,4);
plot(n,x4);
x4[n]'
●3.4节(b)
%计算输出信号并画波形
a=[1-0.25];
b=[10.9];
y1=filter(b,a,x1);
y2=filter(b,a,x2);
y3=filter(b,a,x3);
y4=filter(b,a,x4);
figure;
plot(real(y1(21:
121)));
plot(imag(y1(21:
121)),'
realandimagepartofy1[n]'
plot(y2(21:
121));
y2[n]'
%去掉前20个样本,因为MATLAB脚标从1开始所以取21:
121
plot(y3(21:
y3[n]'
plot(y4(21:
y4[n]'
●3.4节(c)
%判定特征函数
h1=abs(y1(21:
121))./abs(x1(21:
h2=y2(21:
121)./x2(21:
121);
h3=y3(21:
121)./x3(21:
h4=y4(21:
121)./x4(21:
plot(h1);
h1'
plot(h2);
h2'
plot(h3);
h3'
plot(h4);
h4'
7.函数Freqs的使用:
●4.1节
a=[13];
b=3;
freqs(b,a);
w=linspace(0,3*pi);
h=freqs(b,a,w);
plot(w,abs(h));
magnitudeinsomefrequency'
a2=[341];
b2=[105];
freqs(b2,a2);
*8.吉布斯现象:
根据英文教材,验证Fig3.9的吉布斯现象(a)~(d)
N=400;
t=-2:
4/N:
2-4/N;
x=zeros(1,N);
x1=x;
x3=x;
x7=x;
x19=x;
fori=1:
N
ifabs(t(i))<
=1
x(i)=1;
end
x1=0.5+(2/pi)*cos(pi/2.*t);
x3=x1-(2/(3*pi))*cos(1.5*pi.*t);
x7=x3+(2/(5*pi))*cos(2.5*pi.*t)-(2/(7*pi))*cos(3.5*pi.*t);
x19=x7+(2/(9*pi))*cos(4.5*pi.*t)-(2/(11*pi))*cos(5.5*pi.*t)+(2/(13*pi))*cos(6.5*pi.*t)-(2/(15*pi))*cos(7.5*pi.*t)+(2/(17*pi))*cos(8.5*pi.*t)-(2/(19*pi))*cos(9.5*pi.*t);
end
plot(t,x,'
plot(t,x1);
N=1'
plot(t,x3);
N=3'
plot(t,x7);
N=7'
plot(t,x19);
N=19'
%放大后看误差近似0.9%
4.WhatIsYourSenseinTheExperiment?
Intheexperiment,IhavelearnedhowtouseMATLABsolvethequestionsaboutsignalandsystems.Ilearnsomeusefulfunctiontocompletesomecalculation.Ialsolearnedthethepropertiesofsomesystems.
EXPERIMENT2
1.ExperimentPurposes
4.5,(b).
7.1(a)(b)(c)
9.1(c)
9.1(a)(b)
10.2(a)(b)(c)(d)(e)
1.求由微分方程描述的单位冲激响应:
●4.5节(b)。
b1=[1-2];
a1=[11.50.5];
[r1,p1]=residue(b1,a1);
[b2,a2]=residue(r1,p1,0);
%加上真分式的值可以反求出a,b
r1=
6
-5
p1=
-1.0000
-0.5000
2.由欠采样引起的混叠:
●7.1节(a),(b),(c)(补充:
Ω0=2π*5000);
8191];
T=1/8192;
omega=2*pi*1000;
%改变信号频率值,当不满足采样定理时结果不正确。
t=T*n;
xt=sin(omega*t);
xn=sin(omega*n*T);
plot(t(1:
50),xt(1:
50));
x(t)'
stem(n(1:
50),xn(1:
x[n]'
[xrw]=ctfts(xn,T);
plot(w,abs(xr));
ws=8192,wm=1000'
T1=1/8192;
omega=2*pi*5000;
t1=T1*n;
xt1=sin(omega*t1);
xn1=sin(omega*n*T1);
[xr1w1]=ctfts(xn1,T1);
plot(w1,abs(xr1));
ws=8192,wm=5000'
3.作系统的零极点图(用roots和zplane函数):
●9.1节(c)
b=[125];
a=[1-3];
zs=roots(b);
ps=roots(a);
plot(real(zs),imag(zs),'
o'
plot(real(ps),imag(ps),'
x'
用roots函数实现'
gridon;
axis([-44-33]);
zplane(b,a);
用zplane函数实现'
4.求频率响应和极点位置:
●9.2节(a),(b)
b=1;
a1=[101];
a2=[10.51];
a3=[121];
a4=[141];
zplane(b,a1);
H1'
zplane(b,a2);
H2'
zplane(b,a3);
H3'
zplane(b,a4);
H4'
omega=[-5:
0.1:
H1=freqs(b,a1,omega);
plot(omega,abs(H1));
|H1|'
H2=freqs(b,a2,omega);
plot(omega,abs(H2));
|H2|'
H3=freqs(b,a3,omega);
plot(omega,abs(H3));
|H3|'
H4=freqs(b,a4,omega);
plot(omega,abs(H4));
|H4|'
5.离散时间频率响应的几何解释:
●10.2节(a),(b),(c),(d),(e)。
%求零极点图
b1=[100];
a1=[1-0.90.81];
zplane(b1,a1);
ps1=roots(a1);
zs1=roots(b1);
%计算零点矢量和极点矢量的长度和相角
omega=[0:
511]*pi/256;
unitcirc=exp(j*omega);
%在单位圆等分256点,求各点坐标
polevectors1=ones(2,1)*unitcirc-ps1*ones(1,512);
%单位圆上点相对与两个极点的矢量
polelength1=abs(polevectors1);
%极点矢量长度
poleangle1=angle(polevectors1);
%极点矢量相角
zerovectors1=ones(2,1)*unitcirc-zs1*ones(1,512);
%单位圆上点相对与两个零点的矢量
zerolength1=abs(zerovectors1);
%零点矢量长度
zeroangle1=angle(zerovectors1);
%零点矢量相角
plot(omega,zerolength1);
零点矢量长度'
plot(omega,polelength1);
极点矢量长度'
%
geonH1mag=prod(zerolength1)./prod(polelength1);
%零点矢量长度之积除以极点矢量长度之积
geonH1phase=sum(zeroangle1)-sum(poleangle1);
%零点矢量相角之和减去极点矢量相角之积
plot(omega,geonH1mag);
几何方式求解的幅度'
plot(omega,geonH1phase);
几何方式求解的相位'
freqz(b1,a1,512,'
直接用函数求解的响应'
4.WhatIsYourSenseinTheExperiment?
Intheexperiment,welearntoprogramintheMATLAB5.3,includetheprogramflow,softwareenvironment,debugmethod,etc.Wealsorealizesomeprogramstoexaminetheresultwhichwelearnfromthe“SignalandSystem”class.Inaddition,welearnsomeusefulfunctiontocompletesomecalculation.
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