常用函数的拉氏变换和z变换表

常用函数的拉氏变换和z 变换表

时间函数()e t

拉氏变换()E s

Z 变换()E s

单位脉冲δ(t)

1

1

∑∞

=-=0

)()(n T nT t t δδ

Ts

e --11

1

-z z )(1t

s

1 1

-z z t

2

1s 2

)1(-z Tz 2

2

t 3

1s

3

2)1(2)1(-+z z z T

!

n t n

1

1+n s

)(!)1(lim 0aT

n n n a e z z a n -→-∂∂- at

e

-

a

s +1

aT

e z z

-- at

te

- 2

)(1a s +

2

)(aT aT e z Tze ---

at

e --1 )

(a s s a

+ )

)(1()1(aT aT e z z z

e -----

bt

at

e

e

---

)

)((b s a s a

b ++-

bT

aT e z z

e z z -----

t ωsin

2

2ωω

+s

2sin 2cos 1

z T

z z T ωω-+

t ωcos

22ω

+s s 2

(cos )

2cos 1

z z T z z T ωω--+ t e at

ωsin - 2

2

)(ω

ω

++a s

22sin 2cos aT aT aT

ze T

z ze T e ωω----+ t e

at

ωcos -

22)(ω

+++a s a s

222cos 2cos aT aT aT

z ze T

z ze T e ωω-----+

T

t a

/

a

T s ln )/1(1

-

a

z z -