Fonction
Représentation temporelle
Représentation fréquentielle
Pic de Dirac
δ
(
t
)
{\displaystyle \delta (t)}
1
{\displaystyle 1}
Pic de Dirac décalé de
t
0
{\displaystyle t_{0}}
δ
t
0
(
t
)
=
δ
(
t
−
t
0
)
{\displaystyle \delta _{t_{0}}(t)=\delta (t-t_{0})}
e
−
j
.2
π
.
f
.
t
0
{\displaystyle \mathrm {e} ^{-\mathrm {j} .2\pi .f.t_{0}}}
Peigne de Dirac
T
e
=
1
f
e
{\displaystyle T_{e}={\frac {1}{f_{e}}}}
I
I
I
T
e
(
t
)
{\displaystyle \mathrm {III} _{T_{e}}(t)}
I
I
I
f
e
(
f
)
{\displaystyle \mathrm {III} _{f_{e}}(f)}
Fonction porte de largeur
T
0
{\displaystyle T_{0}}
Π
T
0
/
2
(
t
)
{\displaystyle \Pi _{{T_{0}}/2}(t)}
T
0
⋅
s
i
n
c
(
π
.
f
.
T
0
)
{\displaystyle {T_{0}}\cdot \mathrm {sinc} (\pi .f.{T_{0}})}
Constante
1
{\displaystyle 1}
δ
(
f
)
{\displaystyle \delta (f)}
Exponentielle complexe
e
j
.2
π
.
f
0
.
t
{\displaystyle \mathrm {e} ^{\mathrm {j} .2\pi .f_{0}.t}}
δ
(
f
−
f
0
)
{\displaystyle \delta (f-f_{0})}
Sinus
sin
(
2
π
.
f
0
.
t
+
φ
0
)
{\displaystyle \sin(2\pi .f_{0}.t+\varphi _{0})}
1
2.
j
⋅
(
e
j
.
φ
0
⋅
δ
(
f
−
f
0
)
−
e
−
j
.
φ
0
⋅
δ
(
f
+
f
0
)
)
{\displaystyle {\frac {1}{2.\mathrm {j} }}\cdot \left(\mathrm {e} ^{\mathrm {j} .\varphi _{0}}\cdot \delta (f-f_{0})-\mathrm {e} ^{-\mathrm {j} .\varphi _{0}}\cdot \delta (f+f_{0})\right)}
Cosinus
cos
(
2
π
.
f
0
.
t
+
φ
0
)
{\displaystyle \cos(2\pi .f_{0}.t+\varphi _{0})}
1
2
⋅
(
e
j
.
φ
0
⋅
δ
(
f
−
f
0
)
+
e
−
j
.
φ
0
⋅
δ
(
f
+
f
0
)
)
{\displaystyle {\frac {1}{2}}\cdot \left(\mathrm {e} ^{\mathrm {j} .\varphi _{0}}\cdot \delta (f-f_{0})+\mathrm {e} ^{-\mathrm {j} .\varphi _{0}}\cdot \delta (f+f_{0})\right)}
Sinus cardinal
2
⋅
f
0
⋅
s
i
n
c
(
2
π
.
f
0
.
t
)
{\displaystyle 2\cdot f_{0}\cdot {\rm {sinc}}(2\pi .f_{0}.t)}
Π
2
f
0
(
f
)
{\displaystyle \Pi _{2f_{0}}(f)}