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1、
序号
拉氏变换 E(s)
1
1
2
e nsT
3
1
s
4
1
s2
5
1
s3
6
1
s4
7
1
s
(1/ T )ln a
8
1
s
a
9
1
(s
a)2
10
1
(s
a)3
11
a
s( s
a)
12
a
s2 ( s
a)
1
13
( s
a)(s
b)( s c)
2、
s
d
14
( s a)(s
b)( s c)
abc
s( s a)( s b)(s c)
15
16
s2
2
17
s
s2
2
18
s2
2
19
s2
2
2
20
2 )
s(s2
时间函数 e (t)
(t )
(t nT )
u(t)
t
t2
2!
t3
3!
at / T
e at
te at
1 t2e
3、at
2
1 e at
t 1 (1 e aT ) a
e at
e bt
(b
a)( c a)
(a
b)(c
b)
e ct
( a
c)(b
c)
( d
a)
e at
(d
b)
e bt
(b a)( c
a)
(a
b )(c
b )
(a
(d
c)
e
ct
c)( b
c)
1
bc
e at
(c
ca
e bt
(b
a)( c
a )
b)( a
b)
(
4、a
ab
e ct
c)(b
c)
sin
t
cos
t
sinh
t
cosh
t
1
cos t
精品文档
Z 变换 E (z)
1
z n
z
z
1
Tz
5、
( z 1)2
T 2 z( z
1)
2( z
1)3
T 3 z( z2
4 z 1)
6( z
1)4
z
z
a
z
z
e aT
Tze aT
( z
e aT ) 2
6、
T 2ze aT
T 2 ze 2 aT
2( z e aT )2
( z e aT )3
(1
e aT ) z
(z
1)(z
e aT )
Tz
(1
e aT ) z
( z
1)2
a( z
1)(z
e aT )
z
z
(b
a)(c
a)(z
e aT )
(a
b)( c
b)( z
e bT )
z
7、
( a
c)(b
c)( z e cT )
(d
a)z
( d
b) z
(b
a)(c
a)(z
e aT )
(a
b)( c
b)( z
e bT )
(d
c)z
(a
c)(b
c)(z
e cT )
z
bcz
caz
z 1
(b a)(c
a)( z
e aT )
( c
b)(a b)( z e bT )
abz
(a
c
8、)(b
c)(z
e cT )
z sin
T
z2
2zcos
T
1
z( z
cos
T )
z2
2 zcos
T
1
z sinh T
z2
2zcosh
T
1
z(z
cosh
T )
z2
2zcosh
T
1
z
z(z
cosh
T )
z
1
z2
2zco
9、sh
T
1
.
精品文档
21
(s
a)2
2
22
s
a
(s
a)2
2
23
b
a
(s
a )
(s
b)
24
a 2b2
s2 ( s a)(s
b)
e aT sin T
e aT cos T
e at
e bt
abt (a b)
b2
e
aT
a2
e
bT
abTz
(z 1)2
a
b
a
10、 b
ze aT sin
T
z 2
2ze aT
cos
T
e 2 aT
z2
ze aT cos
T
z 2
2ze aT
cos
T
e 2 aT
z
z
z
e aT
z
e bT
(a
b) z
b2 z
a2 z
z
1
( a b)( z
e aT ) ( a b)(z e bT )
.
常用的Z变换公式表
