Home
Add Document
Sign In
Register
Convolución y delta Dirac.pdf
Home
Convolución y delta Dirac.pdf
...
Author:
Florencia Jeandet
6 downloads
226 Views
2MB Size
Report
DOWNLOAD .PDF
Recommend Documents
Delta y Estrella Ejemplos
Full description
Delta
Delta y Estrella Ejemplos
Conexion Delta Delta
Conexiones Delta y Estrella
Descripción completa
Delta-Delta Connection of Transformer
Delta-Delta Connection of Transformer
LABORATORIO 6 Delta y Estrella
laboratorio delta y estrellaDescripción completa
CIRCUITO TRIFASICO FUENTE DELTA Y CARGA DELTA EQUILIBRADO.docx
Delta Abierto
Descripción: practica de laboratorio
CIRCUITO TRIFASICO FUENTE DELTA Y CARGA DELTA EQUILIBRADO.docx
Modulacion Delta
Modulacion delta usando matlabDescripción completa
Delta Phenomenon
Descripción: delta
MODELO DELTA
caso Delta
Delta Profile
delta abierta
delta abierta lab
Star Delta
reportFull description
Delta Beverage
Delta Beverage Case Solution
Modelo-Delta
delta abierta
Descripción: delta abierta lab
Modelo Delta
Delta Dunarii
Delta Abierto
practica de laboratorio
Delta Force
Delta Force rpg by Task Force Games
♠ ♠
δ (t)
t
t
δ (t)
t=0
δ (t) = 0
+∞
−∞
∀ t = 0 δ (t) · dt = 1
t = 0
t = 0
+ δ (t
δ (t) D(t)
− t1)
∞
t1
D(t)
[ β ; +β ] β
−
(2 β )
·
1
β
D(t) D(t)
D(t) =
− 1
β
0 + βt
1
β
β
♣ ♣
t = 0
(t)
β β
−∞)
β
D(t)
β
(
2
t β2
⇔ |t| > β ⇔ −β ≤ t ≤ 0 ⇔ 0 ≤ t ≤ +β
t=0
D(t)
(+ )
β
∞
D(t)
β D(t)
δ (t) = l´ım D(t) β →0
+∞
1=
−∞
δ (t) dt
·
β
ε
·
+∞
1=
−
δ (t) dt =
·
−∞
·
+ε
ε
δ (t) dt +
+∞
δ (t) dt +
·
ε
−∞
−
0
( ε)
−
δ (t) dt
+ε
0
δ (t)
+ε
+∞
1=
(+ )
∞
δ (t)
(
−∞)
+ε
δ (t) dt =
·
−∞
δ (t) dt
·
ε
−
ε ε
+ε
1 = l´ım
ε→0
δ (t
− t0)
δ (t) dt
·
ε
−
t = t 0 δ (t)
t0
α
+ε
1 = l´ım
ε→0
δ (α) dα
ε
−
α=t
− ⇒
α = t
t0
− t0
t0
t = t 0 + α α =
⇒ t = t0 − ε ⇒ t = t0 + ε
−ε
α = +ε dα = dt
t0 +ε
1 = l´ım
ε→0
t0 −ε
δ (t
− t0) · dt
+∞
δ (t
−∞
− t0) · f (t) · dt = f (t)| =
t t0
= f (t0 )
t0 = 0
+∞
−∞
δ (t) f (t) dt = f (t) t=0 = f (0)
·
·
t0
|
ε
+∞
δ (t
−∞
− t0) · f (t) · dt =
(
−∞)
(t0
− ε)
δ (t
−∞
δ (t
t0 +ε
t0 −ε
− t0) · f (t) · dt +
+∞
δ (t
t0 −ε
− t0) · f (t) · dt +
δ (t
t0 +ε
− t0) · f (t) · dt
− t0)
t0 −ε
f (t) dt = 0
·
f (t) dt. = 0
t0 −ε
δ (t
− t0) · f (t) · dt = 0
−∞
(t0 + ε)
+
∞
δ (t
·
−∞
− t0)
+∞
+∞
δ (t
t0 +ε
·
− t0) · f (t) · dt = 0
+∞
·
t0 +ε
t0 +ε
δ (t
−∞
− t0) · f (t) · dt =
δ (t
t0 −ε
− t0) · f (t) · dt
ε ε
ε
+∞
l´ım
ε→0
t0 +ε
δ (t
−∞
− t0) · f (t) · dt = l´ım0 ε→
δ (t
t0 −ε
− t0) · f (t) · dt
ε
+∞
l´ım
ε→0
+∞
δ (t
−∞
− t0) · f (t) · dt =
δ (t
−∞
− t0) · f (t) · dt ε f (t) f (t0 )
ε f (t)
t0 +ε
l´ım
ε→0
·
t0 +ε
δ (t
t0 −ε
− t0) · f (t) · dt = l´ım0 ε→
f (t0 )
δ (t
t0 −ε
− t0) · dt
f (t0 )
·
t0 +ε
l´ım f (t0 )
ε→0
t0 −ε
δ (t
− t0) · dt
t0 +ε
= l´ım f (t0 ) l´ım ε→0
·
ε→0
t0 −ε
t0 +ε
δ (t
− t0) · dt = f (t0) · l´ım0
t0 +ε
l´ım
ε→0
ε→
t0 +ε
δ (t
t0 −ε
t0
− t0) · f (t) · dt = f (t0) · l´ım0 ε→
t0 −ε
δ (t
− t0) · dt
t0 −ε
δ (t
− t0) · dt
t0 +ε
l´ım
ε→0
t0 +ε
δ (t
t0 −ε
− t0) · f (t) · dt = f (t0) · l´ım0 ε→
δ (t
t0 −ε
− t0) · dt = f (t0) · 1 = f (t0)
+∞
δ (t
−∞
− t0) · f (t) · dt = f (t0)
f (t)
g (t)
p(t)
+∞
p(t) =
f (τ ) g(t
· − τ ) · dτ = f (t) ∗ g(t)
−∞
τ t
τ
t
f (τ )
−∞ g (t − τ )
+∞
f (t)
∗ g(t)
=
∗ g(t)
=
∗ g(t)
=
+∞
f (τ ) g (t
−∞
· − τ ) · dτ ∧ f (t) = 0 ∀t < 0 ⇒ f (t) ∗ g(t) =
+∞
f (t)
0
f (τ ) g (t
· − τ ) · dτ ∧ g(t) = 0 ∀t < 0 ⇒
t
f (t)
0
f (τ ) g(t
· − τ ) · dτ t
t = 0
0
f (τ ) g(t
· − τ ) · dτ
f (t)
∗ g(t) = g (t) ∗ f (t) f (t) [g (t) + r (t)] = [f (t) g (t)] + [f (t) r (t)]
∗
f (t)
∗
∗ [g(t) ∗ r(t)] = [f (t) ∗ g(t)] ∗ r(t)
L[f (t) ∗ g(t)] = F (s) · G(s) F (s)
∗
G(s)
f (t)
g(t)
+∞
p(t) = f (t)
∗ g(t)
=
f (τ ) g (t
· − τ ) · dτ
−∞
+∞
q (t) = g (t)
∗ f (t)
γ = t
=
·
t
− → −∞ − → −∞
γ
τ
τ
+ dτ = dγ τ
⇒ γ → +∞ ⇒ γ → −∞
+∞
q (t) = g (t)
∗ f (t)
=
·
− τ ) · dτ ⇒ q (t) =
+∞
+∞
g (t
−∞
⇒ g(t) ∗ f (t)
−∞
g(τ ) f (t
−∞
=
− τ ) · dτ
− τ τ = t
γ = t
g(τ ) f (t
−∞
− γ ) · f (γ ) · dγ =
= f (t) g(t)
∗
g (t
+∞
− γ ) · f (γ ) · (−dγ ) =
f (γ ) g (t
· − γ ) · dγ = f (t) ∗ g(t) ⇒
−∞
f (t) γ
g(t) τ
+∞
f (t)
∗ [g(t) + r(t)] =
−∞
f (τ ) [g(t
·
+∞
f (t)
∗ [g(t) + r(t)] =
−∞
− τ ) + r(t − τ )] · dτ
+∞
f (τ ) [g (t
·
− τ ) + r(t − τ )] · dτ =
−∞
[f (τ ) g (t
· − τ )] + [f (τ ) · r(t − τ )] · dτ
+∞
f (t) [g(t)+r(t)] =
∗
[f (τ ) g(t
· − τ )] + [f (τ · r(t − τ )] · dτ =
+∞
∗ [g(t) + r(t)] =
W (t)
+∞
−∞
f (t)
+∞
f (τ ) g (t
· − τ )·dτ +
−∞
−∞
f (τ ) g (t
· − τ ) · dτ +
f (τ ) r(t
· − τ ) · dτ = [ f (t) ∗ g(t)] + [f (t) ∗ r(t)]
−∞
V (t)
+∞
W (t)
= f (t) g (t) =
∗
f (τ ) g(t
· − τ ) · dτ
−∞
+∞
= g (t) r(t) = r (t) g (t) =
∗
V (t)
∗
r(β ) g(t
· − β ) · dβ
−∞
W (t)
+∞
[f (t) g (t)] r(t) = V (t) r(t) = r (t) V (t) =
∗
∗
∗
∗
= f (t) W (t) =
∗
∗
r(β ) V (t
·
−∞
+∞
f (t) [g (t) r(t)]
∗
f (τ ) W (t
·
−∞
− β ) =
f (τ ) g (t
− τ ) =
r(β ) g (t
− β ) · dβ
− τ ) · dτ
+∞
V (t
· − τ − β ) · dτ
−∞
+∞
W (t
· − τ − β ) · dβ
−∞
+∞
[f (t) g (t)] r(t) =
∗
r(β )
∗
·
+∞
r(β )
−∞
f (τ ) g (t
· − τ − β ) · dτ · dβ
−∞
τ
+∞
[f (t) g (t)] r(t) =
∗
∗
−∞
+∞
r(β ) f (τ ) g (t
f (τ )
∗ [g(t) ∗ r(t)] = f (t) ∗ W (t) =
· − τ − β ) · dτ · dβ
·
−∞
+∞
f (t)
·
+∞
f (τ )
−∞
r(β ) g(t
· − τ − β ) · dβ · dτ
−∞
β
+∞
f (t)
· − τ )·dτ
+∞
−∞
V (t)
f (τ ) r(t
∗ [g(t) ∗ r(t)] = f (t) ∗ W (t) =
−∞
+∞
−∞
f (τ ) r(β ) g(t
·
· − τ − β ) · dβ · dτ
+∞
f (t) [g (t) r(t)] = f (t) W (t) =
∗
∗
∗
+∞
−∞
f (τ ) r(β ) g (t
· − τ − β ) · dτ · dβ
·
−∞
[f (t) g (t)] r(t) = f (t) [g (t) r(t)]
∗
∗
∗
∗
f (t) F (s)
g (t)
G(s)
L[g(t)] = G(s) =
·
+∞
L[f (t)] = F (s) =
f (t) e
st
· dt
g (t) e
st
· dt
·
0
−
+∞
·
0
−
+∞
L[f (t) ∗ g(t)] = P (s) =
+∞
st
[f (t) g (t)] e
∗
0
−
· dt =
0
+∞ st
f (τ ) g(t
· − τ ) · dτ · e · dt
−∞
−
f (τ )
τ
+
∞
+∞
L[f (t) ∗ g(t)] = P (s) =
+∞
0
e
· − τ ) · dτ · e · dt
0
P (s) = f (τ )
t
g (t
+∞
0
st
· − τ ) · e · dt · dτ
0
+∞
P (s) =
g (t)
τ
f (τ ) g (t
0
−
f (t)
st
+∞
st
f (τ ) g (t
−
τ
f (τ )
−∞
−
+∞
0
st
− τ ) · e · dt · f (τ ) · dτ −
t
τ
τ φ = t
− τ φ = t
+∞
P (s) =
0
+∞
0
g (φ) e
·
s(φ+τ )
−
− τ
t = φ + τ dt = dφ
+∞
· dφ · f (τ ) · dτ =
0
+∞
0
g(φ) e
·
sφ
−
sτ
· e · dφ · f (τ ) · dτ
f (t) = 0
−
∀t
< 0
e
−
sτ
φ
+∞
P (s) =
0
+∞ sφ
g (φ) e
·
0
−
sτ
· dφ · e · f (τ ) · dτ −
τ
+∞
L[f (t) ∗ g(t)] = P (s)
=
g (φ) e
·
0
−
t
=
g (t) e
·
0
+∞
dφ
e
sτ
−
0 +∞
+∞
L[f (t) ∗ g(t)]
· · · ·
sφ
st
−
dt
e
st
−
0
· f (τ ) · dτ
· f (t) · dt = G(s) · F (s) = F (s) · G(s)
φ
t
g (t)
τ
f (t)
C (t)
+∞
C (t) =
f (τ ) g (t
· − τ ) · dτ = f (t) ∗ g(t)
−∞
+∞
C (t) = f (t)
∗ δ (t) =
f (τ ) δ (t
· − τ ) · dτ = f (τ )| = = f (t)
−∞
τ t
τ = t
+∞
C (t) = f (t)
∗ δ (t) = δ (t) ∗ f (t) =
τ = 0
t
(−∞)
(+∞)
−∞
δ (τ ) f (t
·
− τ ) · dτ = f (t − τ )| =0 = f (t) τ
F (s)
f (t)
√ j = −1
s = σ + jω
+∞
L[f (t)] = F (s) =
st
f (t) e
·
0
· dt
−
∆(s)
L[δ (t)] =
·
+∞
∆(s) =
δ (t) e
·
0
−
st
· dt
+∞
∆(s) = [δ (t)] =
L
0
δ (t) e
st
−
· dt = e
st
−
t=0
= e 0 = 1
×
Report "Convolución y delta Dirac.pdf"
Your name
Email
Reason
-Select Reason-
Pornographic
Defamatory
Illegal/Unlawful
Spam
Other Terms Of Service Violation
File a copyright complaint
Description
×
Sign In
Email
Password
Remember me
Forgot password?
Sign In
Our partners will collect data and use cookies for ad personalization and measurement.
Learn how we and our ad partner Google, collect and use data
.
Agree & close
