00
jsg

22
ej0t
20
etcosttetsi
tt
jj22
j22
常用连续傅里叶变换、拉普拉斯变换、Z变换对一览表
拉普拉斯变换对（单边）
Fsftestdt0
函数
象函数
ft
Fs
t
1
ttttt
tetttettcosttsi
ttcoshttsi
httetcosttetsi
tt
s
1s
1
s2s
1
1
1
ss2
ss22
s22
ss22
s22
ss22
s22
函数fkk0
k
1
k
kk
akkekkejkkakakk2akk1k2akbkkabcoskk
Z变换对（单边）

Fzfkzkk0
象函数
函数
fkk0
1
kmm0
zz1
zz1
zz12
zza
zze
zzej
zz2a2
zz13
zzazb
zzcosz22zcos1
kmm0k2k
k1akkkak1kkakkk2akk
akakk2a
k1kk2
ak1bk1kab
si
kk
象函数
zm
zzmz1
z2zz13
z2za2
zza2
azza2
az2a2zza3
z2z2a2
z2z13
z2zazb
zsi
z22zcos1
fett0tt

222
j22j

sg
t
2
j
eetttt000
j222
f
t

cos0t
t
2

t

2

F
ej
t

2

cos2
2
2
2
2
2

F






2T

Ttt
T




2T
g
t


1t0t
22
Sa2si
22
b0tb1t
b0
b0
b1ett
1tsi
tt3
12
3
1

t
si
t

t

1tsi
tt21si
ttcostt2
tcostt
b0b1tb1et
b0b1ss2
b1sb0ss
1s2s22
1s222
ss222
s2s222
s22s222
b1sb0s2
coskkakcoskkakcoshkk
z2coszcosz22zcos1
zzacosz22azcosa2
zzacoshz22azcosha2
si
kkaksi
kkaksi
hkk
z2si
zsi
z22zcos1
azsi
z22azcosa2
azsi
hz22azcosha2
akkk0k
l
zza
akkk
a
ez
l
akkk1k
k1
1
az
zl
zz1
12k
1k2k1
cosh1z
1zl
z1
2
z1
b0b1etb0b1ett


b1sb0ss
b0b1b22etb0b1b22et


b0b1b22ett
b2s2b1sb0sss
WSaWtsi
Wt

t
f
t

10
2t
t2
t

2
F

j

10

W2W2
Sa224
Aetsi
tt其中Aejb0b1j

b2etb12b2tet
12
b0

b1

b2
2
t2et
t
b1sb0s22
b2s2b1sb0s3
b0b1b22etb0b1b22tet
2

b0b1b22ett2
b0b1b22etAsi
tt22
其中Aejb0b22jb1j
b2s2b1sb0s2s
b2s2b1sb0ss22
ff
t

1
t

0t
2
2
t

2
j
1
e
j
2

Sa



2
1

t

12
f
t


1
1
2t
12
t

2


0t

2

2
8
1
si


4
1r