第5章 数字滤波器结构及实现
5-1 写出题图5.1结构的传递函数及差分方程。
解:(a)
y(n)=0.25 y(n-1)-0.3 y(n-2)+2 x(n)+0.25 x(n-1)
21
1
3.025.01
25.02
)(
−−
−
+−
+
=
zz
z
zH
(b)
21
21
1
1
5.05.11
25.01
)(
)(
)(
−−
−
−
−−
++
==
zz
zz
zX
zX
zH
)()(
21
zXzY =
)(
2.01
1
)(2.0)()(2.0)()(
1
1
2
1
11
1
12
zX
z
zXzzXzYzzXzX
−
−−
+
=
−=−=
注意X2(z)有2个输入,所以不等于X1(z)
21 2
2
1
11 1
() 2 () 2 () 2
()
() () () 1 0.2
Yz Yz X z
Hz
X
zXz Xz z
−
== = =
+
12
33
2
3
12
121
() ()
()
42 1
()
() () () 1 0.2 0.8 1 0.2
Yz Yz
Xz
zz
Hz
Xz Xz Xz z z z
−−
1
−
−−
++
==⋅= ⋅
−+ +
23
11
12 3
11
12 12
12 1 12 1
12 1 2
12
() ()
() () ()
() ()[ () ()]
() () () ()
10.5 2 2 4 2 1
[]
1 1.5 0.5 1 0.2 1 0.2 0.8 1 0.2
10.5 2 60.6 3.6
1 1.5 0.5 1 0.76
Yz Yz
XzYz Xz
H
zH
Xz X z Xz X z
zz zz
zz z zz z
zz z z
zz z
−− −−
−− − −− −
−− − −
−− −
zHzHz
+
⋅
==•=+
⋅
++ ++
=+⋅
−− + −+ +
++ ++
=⋅
−− +
23
1234
12345
0.16
6 3.6 15.9 3 7.2
1 1.5 0.26 0.98 0.62 0.08
z
zzzz
zzzzz
−
−−−−
−−−−−
+
++ ++
=
−+ − − −
y(n)=1.5y(n-1)-0.26y(n-2)+0.98y(n-3)+0.62y(n-4)+0.08y(n-5)
+6x(n)+3.6x(n-1)+15.9x(n-2)+3x(n-3)+7.2x(n-4)
1