Example Reference Sheet
1
7/17/2019 Example Reference Sheet http://slidepdf.com/reader/full/example-reference-sheet 1/1 Table 4.2 Table 6.2 Fo u rier Transform Operations Operation ft F w Addition t +f t F w + F w Scalar multiplication kf t kF Symmetry Ft 2irf —w Scaling a real f at L ) l Time shift f t F w e_3L t0 Frequency shift wo real f t e3P0t F w — wo Time convolution f 1 t * f 2 t Fj w F Frequency convolution f t f t —F 1 w * w Time differentiation j ”F Time integration f x dx + ir F O b Fourier Transform airs 6 t 1. u t irö w + iw _L fora > _atzi t <=> a+jw Laplace Transform a irs 6t u t 1 e_atu t 4=zz s+a te_atu t s±a 2 8+a _at cos bt u t s+ a b _at sin b t u t s+ a b The Laplace Transform Properties Operation f t F s Addition t +f t F s +F s Scalar multiplication kf t kF s Time differentiation sF s — f Oj s s sf 0 f O j s s s Oj sf Oj f Oj Time integration f T dr iF s ,t ‘° f r dr —F s + ft dt J—oo J—oo Time shift ft to u t F s e_3t0 t 0 Frequency shift f t e30t F s — so dF s Frequency —tf t ds differentiation Frequency integration Fz dz c ling f at , a 0 .LF Time convolution f 1 t * f 2 t Fi s F s Frequency convolution f t f t — -— F s * F s 2irj Initial value f O j lirnsF s n > m Final value f oo lim sF s poles of sF s in LHP s
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Example Reference SheetExample Reference SheetExample Reference SheetExample Reference SheetExample Reference Sheet
Transcript of Example Reference Sheet
7/17/2019 Example Reference Sheet
http://slidepdf.com/reader/full/example-reference-sheet 1/1
T
able
4
.2
Tab
le
6.2
Fou
rier
Tr
ansfo
rm
Oper
atio
ns
O
pera
tion
f t
F w
Addition
t +ft
F
w +
F
w
Scalar
mu
ltip
licat
ion
kf
t
kF
Symmetry
F
t
2irf —w
Scaling
a
real
f
a t
L
)
l
Time
shift
f t
F w e_3L t0
Frequency
shift
wo
real
f t e3P0t
F w
—
wo
Time
convolution
f1
t
*
f2
t
F
j w F
Frequency
convolution
f
t
f
t
—
F
1w
*
w
Time
differentiation
j ”
F
Time
int
egra
tion
f x dx
+
irF
O b
Fo
urie
r
T
ransf
orm
a
irs
6 t
1.
u
t
irö
w
+
iw
_L
fora
>
_
atzi
t
<
=>
a+jw
Lapl
ace
Tra
nsfo
rm
a
irs
6 t
u
t
1
e
_atu
t
4=zz
s+a
t
e_atu
t
s±a 2
8+a
_a
t
cos
bt u
t
s+ab
_a
t
si
n b t
u t
s+
a
b
The
Lap
lace
Tran
sform Pro
perti
es
Ope
ratio
n
f
t
F s
Addition
t +f
t
F
s +F
s
Scalar m
ultip
lica
tion
kf
t
kF s
Time
differentiation
s
F s
—
f
Oj
s
s s
f 0
f
O j
s s
s
Oj sf
Oj
f
O j
Time
integration
f T
dr
iF s
,t
‘
°
f r
dr —F s
+
f
t
dt
J—oo
J—oo
Time
shift f t
to
u t
F
s e_
3t0
t
0
Frequency
shift
f t e30t
F
s
—
so
dF s
Frequency
—tf t
ds
differentiation
Frequency in
tegr
ation
F
z
dz
c ling
f a
t ,
a
0
.LF
Time
convolution
f
1
t
*
f
2
t
Fi s
F
s
Frequency convolution f
t ft —
-— Fs
*
Fs
2irj
Initial
value
f O
j lirn
sF
s
n
>
m
Final
value f oo
lim
sF s
poles of
sF s
in
LHP
s
