Comunicación Bluetooth entre un dispositivo Mobil y un microcontrolador.
Tabla de Dualidad Transformada Z, Transformada de LaPlace y Discreta.
1. TABLAS DE TRANSFORMADA Z
( )f t F. Continua
( )f kT F. Discreta,
muestreada
( )F s Transforma de
Laplace
( )F Z Transformada Z
( )t
Impulso de Dirac
( )kT 1 1
( )t T ( )t kT * TS
e
( )t
Escalón Unitario
( )kT
1
S 1
Z
Z
( )t T ( )t kT *
TS
e
S
( )t kT T
SkT T S
e
S
t
Rampa
kT 2
1
S
2
( 1)
Tz
z
2
t
2
kT 3
2
S
2
3
( 1)
1
T z z
z
3
t
3
kT 4
6
S
3 2
4
( 4 1)
1
T z z z
z
21
2
t
21
2
kT 3
1
S
2
3
( 1)
2 1
T z z
z
1m
t
;
1,2,3,...m
( 1)!
m
m
s
1
1
10
lim ( 1)
m
Tt
m
mb
z
z e
b
at
e akT
e
1
S a aT
Z
Z e
at
te akT
kTe
2
1
S a
2
aT
aT
Te z
z e
2 at
t e
2 akT
kT e
3
2
S a
2
3
( )aT aT
aT
T e z z e
z e
sin( )bt sin( )bkT 2 2
b
s b
2
sin( )
2 cos( ) 1
z bT
z z bT
cos( )bt cos( )bkT 2 2
S
S b
2
2
sin( )
2 cos( ) 1
z z bT
z z bT
sin( )at
e bt
sin( )akT
e bkT
2 2
( )
b
S a b 2 2
sin( )
2 cos( )
aT
aT aT
ze bT
z ze bT e
cos( )at
e bt
cos( )akT
e bkT
2 2
( )
S a
S a b
2
2 2
cos( )
2 cos( )
aT
aT aT
z ze bT
z ze bT e
2. cos( )at
e t
cos( )akT
e kT
2 2
cos( )( ) sin( )
( )
S a
s a
2 2
cos( )( ) sin( )
( )
z z z
z
Donde:
cos( )
sin( )
aT
aT
e T
e T
1 at
e
1 akT
e
( )
a
S S a
1
1
aT
aT
e z
z z e
1 (1 ) at
at e
1 (1 ) akT
akT e
2
2
( )
a
S S a
1
1
aT
aT aT
z ate
z z e z e
at bt
e e
akT bkT
e e
( )( )
b a
S a S b
( )
( )( )
aT bT
aT bT
e e z
z e z e
bt at
be ae
bkT akT
be ae
( )( )
b a S
S a S b
( ) ( )
( )( )
aT bT
aT bT
b a z be ae z
z e z e
(1 ) at
at e
(1 ) akT
akT e
2
( )
S
S a
2
(1 ) aT
aT
z aT e z
z e
1 at
at e
1 akT
akT e
2
( )
a
S a S 2
( 1 ) (1 )
( 1)
aT aT aT
aT
aT e z e aTe z
z z e
bT at
e e
a b
1
( )( )S a S b
1
bT aT
z z
a b z e z e
1
(1 )aT
e
a
1
( )S S a
1 (1 )
( 1)
aT
aT
e z
a z z e
1 1
( )
aT
e
t
a a
2
1
( )S S a 2
1 (1 )
( 1) ( 1)
aT
aT
Tz e z
a z a z z e
k
a
z
z a
1k
a
1k
1
z a
1k
ka
2
z
z a
2 1k
k a
3
( )z z a
z a
3 1k
k a
2 2
4
( 4 )z z az a
z a
k
a
z
z a
3. cos( )k
a k
z
z a
2
( 1) k
k k a
3
2z
z a
( 1)...( 2)k k k m
( 1)!
( 1)m
z m
z
21
( 1)
2
k
k k a
3
( )
z
z a