N=60
a=[1 -1 0 0.9];
b=[1 0 0 0 ];
subplot(131);
impz(b,a);
subplot(132);
impz(b,a,N);
subplot(133);
impz(b,a,-10:1:40);
a=[1 -1 0 0.9];
b=[1 0 0 0 ];
y=impz(b,a,-5:1:10)
y = 0
0
0
0
0
1.0000
1.0000
1.0000
0.1000
-0.8000
-1.7000
-1.7900
-1.0700
0.4600
2.0710
3.0340
%10.5
N=30;
a=[1 0.4 -0.12];
b=[1 2];
f=ones(1,N);
k=0:1:N-1;
zi=filtic(b,a,[1,2]);
yf=filter(b,a,f);
y=filter(b,a,f,zi);
subplot(211);
stem(k,yf);xlabel('k');title('零状态响应yf(k)')
subplot(212);
stem(k,y);xlabel('k');title('全响应y(k)')
%11.1
1.syms n;
f=sym('Heaviside(n)');
F=ztrans(f);
simplify(F)
ans =z/(z-1)
2.syms a n;
f=a^n;
F=ztrans(f)
'f=',pretty(f);
'F=',pretty(F);
f= n
a
ans =
F= z
-----------
a (z/a - 1)
3.syms n;
f=sym('0.5*n*(Heaviside(n)-Heaviside(n-5))');
F=ztrans(f)
'F=',pretty(F);
F =.5/z^4*(z^3+2*z^2+3*z+4)
F= 3 2
z + 2 z + 3 z + 4
0.5 -------------------
4
z
4.syms a n;
f=a^n*cos(n*pi/2);
F=ztrans(f)
'F=',pretty(F);
F =z^2/a^2/(z^2/a^2+1)
F= 3 2
z + 2 z + 3 z + 4
0.5 -------------------
4
z
F=
2 z
-------------
/ 2 \
2 | z |
a |---- + 1|
| 2 |
\\ a /
%11.2
1.syms n;
f=(-1)^n;
h=1/3*(-1)^n+2/3*(3)^n;
F=ztrans(f);
H=ztrans(h);
yf=iztrans(H*F)
yf=1/2*3^n+1/2*(-1)^n+1/3*(-1)^n*n
2.syms n z;
f=1^n;
F=ztrans(f);
H=z*(7*z-2)/(z-0.2)/(z-0.5);
yf=iztrans(H*F)
yf =25/2-5*(1/2)^n-1/2*(1/5)^n
%11.3
syms z;
H=z^2/(z^2+sqrt(2)*z+1);
h=iztrans(H)
h =cos(3/4*n*pi)-sin(3/4*n*pi)
n=-10:20;
h=(cos(3/4*n*pi)-sin(3/4*n*pi)).*(n>=0);
stem(n,h,'filled')
title('单位序列响应h(n)')
xlabel('n')
num=[1 0 0];
den=[1 sqrt(2) 1];
z=roots(num)
p=roots(den)
zplane(z,p)下载本文
