Tarea Semana 3
February 19, 2023 | Author: Anonymous | Category: N/A
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UNIVERSIDAD TECNOLOGICA IS
Nombre Steven Hidalgo
Tarea 3
Y(n)=x(n)+(−)/
(−)
y(n)=0,8y(−)+3x(n-1)+2x(n)
(−)
y(n)=x(n)+0,9y(−)+3x(n-2)+2x(n-1)
Y(n)=/(x(n-3)+())+ ((n-1))
y(n)=/y(n-1)+/ + (n-2)
(−) /
y(n)=0,8x(n-1)+x(n) +0,6(−)
_(n)=_ ()+_ (−)+_ (−)
_(n)=_ ()+_ (−)+_ (−)
_(n)=_ ()+ ()+ 〖 ( 〗 _+ _+_ _ _) _)(− (−)+ )+_ _ _ (−)
Y(n)=/y(n-1)+x() +(n-1)
RAEL
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y(n)=[()]=(^
)
) . y(2)=(2^2 ) y(2)=(4) x(n)=y()=(^2)
EL SISTEMA ES VARIANTE EN EL TIEMPO
x(n-k)=_1 ()=(−)^2
x(n-k)=_ ()≠(−)
) ()=[()] .) (0)
x(n-k)=_1 ()=(^2+^2−2) ) ()
ñ.
.)_1 ( ( _2 ( (
() ()
_3 ()
) ñ () x()={0,⏟,1,1,1,0…}
_3 ( ()= )=_ _ _3 (
((
.)(,
(−)
((−)"
(,)
) ñ ()=[()]
.)
y()=(^2)={…,0,1,⏟,1,0…}
.)(
) ñ _^(´^′ ) ()=(−).
( (1
y(−2)={…0,⏟,11,1,0…}
( (
) ñ _ ()=(−).
) ()=()(_ )
x(−2)={…⏟,0,11,1,1,0…}
) ñ _ ()=[_ ()].
1.
_2 ()=[x(−2)"]"={…0,1,0,⏟,0,1,0…}
) ñ _ () () (−). ¿ ? . _ ()≠(−)
2.
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_ ()≠(−) Variante en el empo )
() .
3.
_1
¿ ?¿? .
_3 _3 (
x()={⏟,1,1,1}
y()={⏟,0,0,0,0,−1}
y(−2)={⏟,0,0,1,0,0,0,0,−1}
4. 5.
x(−2)={⏟,0,1,1,1,1,1,}
_2 ()={⏟,0,1,0,0,0,0,−1}
_ ()=(−) INVARIANTE EN EL TIEMPO
)
() () .
x()={…..,0,⏟,1,1,1,0…..} y()={…..,⏟,1,2,3,…….}
) ()=(−+)
1.
2.
y(−2)={…..,⏟,0,0,1,2,3,…….}
_3 ()= x(−2)={…..,0,⏟,0,1,1,1,1,…….}
_2 ()=[x(−2)"]"={…0,0,2,3,4,5…}
_(
3.
(−+
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(−+
_ ()≠(−) VARIANTE EN EL TIEMPO 4. 5.
) ()=|()| 1.
()=(() _1 () _2 ()
2. 〖 ( 〗 _3 ()= 3.
(, ( (,
4. 5.
( () (0)= (1)= (2)=
) ()=()() 1.
(2)
2.
_3 ()= ´
( (
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_
3.
4. 5.
(
) ()=()+(+) 1.
x( x(3
2.
( 3.
_1 ( _2 ( _3 ()=[
_ _3 3 (() )=[ =[_ _ _3 ( +3( _3 ( 4. 5.
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) ()=() ) ()={█((), ()≥@, ) ()=(−)
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) ()=[()] .)
=((0))
.)
=(_1 () )
) =(_2 ()
ESTATICO
(_1 _1 ()+_2 _2 ())(()) 1 _1 ()(()")" _2 _2 ()(()")" LINEAL (()")" )=_1 _1 ()+_2 _2 ()=_1(_1 ()(()")"+_2(_2 ()
.)
)=[(−)]=(()")" =((−)")" (−)
.) . .)
INVARIANTE CAUSAL
= )=(()) =(1()) )=(2()) )=(3()) ESTABLE
) ()=()(_ ) (0)=(0)(_0 0)
ESTATICO
(1)=(1)(_0 1)
(,)=[(−)]=(−)(_ n) (−)=(−)(_ (n−k ))
VARIANTE
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(,)≠(−) ()=_1 ()(_ )
LINEAL
2 ()=_2 ()(_ ) ()=(_1 _1 ()+_2 _2 ())(
_
)
)=_1 _1 ()(_ )+_2 _2 ()(_ ) _3 ()=_1 _1 ()+_2 _2 ()=_1(_1 ()(_ ))+_2(_2 ()(_ )) CAUSAL POR QUE ES ESTATICO
()=
CAUSAL ESTABLE
()=(_0 )
(1)=(_0 1) (2)=(_0 2) (3)=(_0 3)
) ()=(−+) ()=(−2+2) ()=(0)
DINAMICO
_1 ()=_1 (−+2)
LINEAL
_2 ()=_2 (−+2)
〖 ( 〗 _1 _1 ()+_2 _2)+ 〖 _1 〗 _1 (−+2)+_2 _2 (−+2))
3) ()=_1 _1 ()+_2 _2=_1 (_1 (−+2))+_2 (_2 (−+2))
(,)=[(−)]=(−+2) − =(−+)
VARIANTE
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(−+) (,)≠(−) NO CAUSAL POR SER DINAMICO
()=()
NO CAUSAL ESTABLE
()=(−+2) (0)=(2)=2 (1)=(3)=2 (2)=(8)=2
) ()=|()| ()=(())
=_1 ()
=_2 ()
ESTATICO
_1 _1 ()+_2 _2 ())+ 〖 _1 〗 _1 ()+_2 _2 ()) )=[(−)]= (()")"
NO LINEAL INVARIANTE
)=[(−)]=((−)")" )=(−) CAUSAL POR QUE ESTATICO
CAUSAL
)=()
ESTABLE
=() 0)=1 1)=1 2)=1
) ()=()() =(2)(2)
ESTATICO
_1 ()=()())
LINEAL
_2 ()=()() ( 〗 _1 _1 ()+_2 _2 ())+ 〖 _1 〗 _1 ()()+_2 _2 ()()
=
=
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_
_
_
_
_
_
_
(,)=[(−)]=(−)(−)
_
INVARIANTE
(−)=(−)(−) (,)=(−) CAUSAL POR QUE ESTATICO
CAUSAL
()=()()")"
ESTABLE
)=()()")" (0)=(0)(0)")"=1 (1)=(1)(1)")"=1 (2)=(2)(2)")"=1
) ()=()+(+) )=(3)+3(3+1)
DINAMICO
)=(3)+3(4) (,)=[(−)]=(−)+3(+1)
VARIANTE
−)=(−)+3(−+1) −)≠(,) )=_1 ()+3(+1)
LINEAL
)=_2 ()+3(+1) _1 _1 ()+_2 _2 ()]^2=_1 ()+_2 ()+3(+1)
1 _1 ()+_2 _2 ()]^2=_1 ()+_2 ()+3(+1)
)=[_1 _1 ()+_2 _2 ()]^2=_1 ()+_2 () +1) = 〖 ´ 〗 _3 () NO CAUSAL PORQUE ES DINAMICO
()=() ()=()−3(+3) (0)=(0)−3(0)(0+3)=1 (1)=(1)−3(1)(+2)=1 (2)=(2)−3(2)(+1)=1
NO CAUSAL INESTABLE
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(3)=(3)−3(3)(0)=−11 (4)=(4)−3(1)=−15
) ()=() █((), ()≥@, ) ()=(−)
()
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