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94
Приложение 1
ТАБЛИЦА СИГНАЛОВ И ИХ СПЕКТРОВ
Сигнал s(t) Спектр сигнала C( f )
t
0
2
τ
− 2
τ
A
() ()
tAts
τ
rect⋅=
f
0
τ
A
() ( )
τπτ
fAfC sinc⋅=
τ
1
τ
1
−
t
0
α
1
A
() ()
tuAts
t
⋅⋅=
⋅−
α
e
f
0
σ
21
A
()
f
A
fC
πα
2+
=
σ
21−
()
fC
()
fCarg
2
π
t
0
σ
3
A
()
2
2
2
e
σ
t
Ats
−
⋅=
σ
3
f
0
σ
21
πσ
2A
()
()
2
2
e2
σπ
πσ
f
AfC
⋅−
⋅=
σ
21−
t
0
A
() ( )
tfAts
0
2cos
π
⋅=
0
T
f
0
()
2A
() ()(){
}
00
2
ffff
A
fC −++⋅=
δδ
0
f
0
f−
()
2A
t
0
A
() ( )
tfAts
0
2sin
π
⋅=
00
1 fT =
f
0
()
2jA
() ()(){}
00
2
ffff
jA
fC
−−+⋅=
δδ
()
2jA−
00
1 Tf =
0
f−
t
0
()
A
() ()
tAts
δ
⋅=
f
0
A
()
AfC =
t
0
)(A
() ( )
∑
∞
−∞=
−⋅=
n
nTtAts
δ
T 2T -T -2T
t
0
()
∑
∞
−∞=
−⋅=
k
T
n
f
T
A
fS
δ
T1 T2T1−T2−
T
A
Приложение 1
ТАБЛИЦА СИГНАЛОВ И ИХ СПЕКТРОВ
Сигнал s(t) Спектр сигнала C( f )
s(t ) = A ⋅ rect τ (t ) C ( f ) = Aτ ⋅ sinc(π f τ )
Aτ
A
1 1
−
τ τ
t f
−τ 2 0 τ 2 0
A
s(t ) = A ⋅ e −α ⋅t ⋅ u (t ) C( f ) =
A α + 2π f
A arg C ( f )
C( f )
π 2
f
t
− 1 2σ 0 1 2σ
0 1α
C ( f ) = Aσ 2π ⋅ e −2⋅(π f σ )
t2 2
−
s(t ) = A ⋅ e 2σ 2
A Aσ 2π
t f
3σ 0 3σ − 1 2σ 0 1 2σ
s(t ) = A ⋅ cos(2π f 0t ) A
A C( f ) = ⋅ {δ ( f + f 0 ) + δ ( f − f 0 )}
2
t ( A 2) ( A 2)
0
T0 f
− f0 0 f0
s(t ) = A ⋅ sin (2π f 0t ) jA
C( f ) = ⋅ {δ ( f + f 0 ) − δ ( f − f 0 )}
A 2
t ( jA 2)
0
f 0 = 1 T0 f
T0 = 1 f 0
− f0 0
(− jA 2)
s(t ) = A ⋅ δ (t ) C( f ) = A
( A) A
t f
0 0
∞
A ∞ n
s(t ) = A ⋅ ∑ δ (t − nT ) S( f ) = ⋅ ∑ δ f −
T k =−∞ T
(A)
n =−∞ A
T
t t
-2T -T 0 T 2T − 2 T −1 T 0 1T 2T
94
