Добавил:
Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:

метода цос

.pdf
Скачиваний:
120
Добавлен:
15.03.2015
Размер:
1.14 Mб
Скачать

(1><:(#1 +:/<. 1.4, ((+1</$2 3 0*" a1 $ 0,8 ), : +:)9$ (81%(+8- <"#$%- #1(+" Z- 0*$1/*:;18:#"? " +$1*$,$ 1 ;:'$*9)$ *:8$#

 

x (n) $ 0,5 G 0,8n)1 .

 

 

 

2

 

x1(n) "

F()1,&% 1*">"#:< *:8$# (-,,$ 01(<$'18:+$<=#1(+$%

x2 (n) :

 

 

 

 

x(n) $ x (n) # x (n) $ 0,2 G 0,8n # 0,5 G 0,8n)1 .

(1.40)

1

 

2

 

 

3 -.$+1, #-<$8&@ #:.:<=#&@ -(<18"% 1*">"#:< x(n) 10*$'$<?-

$+(? (<$'-AS", 1/*:;1,:

 

 

 

 

'0,2 G 0,8n ,

n $ 0;

 

x(n) $ &0.2 G 0,8n #

0,5 G 0,8n)1, n 1 0,

 

%

 

 

 

 

01()1<=)- 0*" n $ 0 ;#:.$#"$ x2

$ (n) 10*$'$<?$+(? 8 1/<:(+" 1+-

*"2:+$<=#1>1 8*$,$#"

 

(n )1) $ )1

 

 

 

 

", (<$'18:+$<=#1, 0*" #-<$8&@ #:.:<=#&@ -(<18"?@

 

x

 

(0) $ 0,5 G 0,8)1 $ 0 .

 

2

 

 

 

1.4.2. B.7./<8:K0<D G?06I1D. $::80:S.01. -T://-4T:/

K(#18#1% @:*:)+$*"(+")1% !G3 8 z-1/<:(+" ?8<?$+(? z-";1- /*:9$#"$ ",0-<=(#1% @:*:)+$*"(+")" h(n)

H (z) $ ZEh(n)F,

(1.41)

)1+1*1$ 10*$'$<?$+(? 01 C1*,-<$ @+95'1' Z-0*$1/*:;18:#"? (1.22)

-

H (z) $ ,h(n)z)n . (1.42)

n$0

4*" ";8$(+#1, z-";1/*:9$#"" H (z) ",0-<=(#:? @:*:)+$*"(+"-

): h(n) #:@1'"+(? ( 01,1S=A ',+3=2'1' Z-0*$1/*:;18:#"?

 

h(n) $ Z )1EH (z)F,

(1.43)

>'$ H (z) #:;&8:A+ @.+.;3='B2': 672&80.: (4L) !G3; R+1 ,:+$,:-

+".$()1$ 10*$'$<$#"$ 4L.

/''=2'P.20. (H';/($H'; !G3 81 (+.5.22': 1/<:(+" 10"(&8:-

<1(= ( 01,1S=A C1*,-<& (8$*+)", <"/1 8 8"'$ *:;#1(+#1>1 -*:8#$- #"?. B:((,1+*", 011.$*$'#1 "@ 1+1/*:9$#"$ 8 z-1/<:(+".

Q'+574. <(.+=&0 ((,. 0. 1.3.1)

31

 

'

-

 

 

D

,h(n ) m)x(m);

 

y(n) $

D

 

 

&m-$0

 

 

DD

, x(n ) m)h(m),

 

 

%m$0

 

8 z-',43<=0 (11+8$+(+8-$+ -*:8#$#"$ ((,. 0. 1.4.1)

 

Y (z) $ H (z) X (z) ,

(1.44)

>'$ X (z) " Y (z) – z-";1/*:9$#"? 81;'$%(+8"? " *$:)2"".

J: 1(#18:#"" (1.44) 0$*$':+1.#-A C-#)2"A ,19#1 0*$'(+:- 8"+= ):) 1+#1O$#"$

H (z) $

Y (z)

,

(1.45)

X (z)

 

 

 

)1+1*1$ 01;81<?$+ $$ 10*$'$<"+= 01'1/#1 0$*$':+1.#1% C-#)2"" <"#$%#&@ :#:<1>18&@ ("(+$,.

A.3.4&1",$"/ :6$52%./ H (z) !G3 #:;&8:$+(? '=2'P.20.

z-0F',+3%.209 +.3&800 & z-0F',+3%.20A ('F;.:<=(09 @+0 274.($H 23B34-2$H 7<4'(09H.

G:##1$ 10*$'$<$#"$ 4L #$ 0*1+"81*$."+ 0*"8$'$##1,- ,:+$- ,:+".$()1,- (1.42). G$%(+8"+$<=#1, (1><:(#1 10*$'$<$#"A, ",- 0-<=(#:? @:*:)+$*"(+"): h(n) $(+= *$:)2"? #: 81;'$%(+8"$ 8 8"'$

2"C*181>1 $'"#".#1>1 ",0-<=(: u0 (n) .

41'(+:8"8 z-";1/*:9$#"? ':##&@ 81;'$%(+8"? " *$:)2"" 8

(1.45) " -."+&8:?, .+1 Z{u0 (n)} $ 1

((,. +:/<. 1.4), 01<-.", 10*$'$-

<$#"$ 4L (1.42):

 

 

 

H (z) $

Y (z)

$

Z{h(n)}

 

$ Z{h(n)}.

 

 

 

X (z) Z{u0 (n)}

 

#3F2'<=2'57 7+3(2.20A (1.15)

 

 

 

 

N )1

M )1

 

y(n) $ ,bi x(n ) i) ) ,ak y(n ) k)

 

i$0

k $1

 

8 z-',43<=0 (11+8$+(+8-$+ -*:8#$#"$, )1+1*1$ ,19#1 01<-."+=, 8&-

01<#"8 Z-0*$1/*:;18:#"$ 0*:81% " <$81% .:(+$% B6:

 

'N )1

M )1

V

ZEy(n)F$ Z & ,bi x(n ) i) )

,ak y(n ) k)U .

% i$0

k $1

T

32

 

 

F(01<=;-? (81%(+8: Z-0*$1/*:;18:#"? (<"#$%#1(+= " +$1*$,- 1 ;:'$*9)$), ;:0"O$,

 

N )1

M )1

Y (z) $

X (z) , bi z)i )Y (z) , ak z)k ,

 

i$0

k $1

1+)-': 01(<$ 0*"8$'$#"? 01'1/#&@ ",$$, 341.,+30B.<&'. -*:8#$#"$

 

N )1

 

 

 

, bi z)i

 

 

Y (z) $

i$0

X (z) .

(1.45:)

M )1

 

 

 

 

1# , ak z)k

 

 

k $1

B:;'$<"8 1/$ .:(+" R+1>1 -*:8#$#"? #: X (z) , 01<-.", 0$*$':- +1.#-A C-#)2"A ',E.1' (0;3

 

N )1

 

 

 

, bi z)i

 

 

H (z) $

i$0

.

(1.46)

M )1

 

 

 

 

1# , ak z)k

 

 

k $1

4L (1.46) 0*$'(+:8<?$+ (1/1% '*1/#1-*:2"1#:<=#-A C-#)2"A,

."(<"+$<= " ;#:,$#:+$<= )1+1*1% ?8<?A+(? ,#1>1.<$#:," 1+#1("- +$<=#1 z)1 01*?')18 (N )1) " (M )1) (11+8$+(+8$##1 ( (.E.<=(.2- 2$50 )1RCC"2"$#+:," bi " ak . 3<$'18:+$<=#1, 4L ;:8"("+ "()<A-

."+$<=#1 1+ 8#-+*$##"@ 0:*:,$+*18 !G3 ((,. 0. 1.3.2) " #$ ;:8"("+ #" 1+ 81;'$%(+8"?, #" 1+ *$:)2"".

I'+9;&'5 IQ #:;&8:A+ #:"/1<=O$$ "; ."($< (N )1) " (M )1) .

U'$(= " ':<$$ 01<:>:$,, .+1 @'+9;'& 52'1'B4.23 B0<40=.49 2. @+.- ('<H';0= @'+9;&3 52'1'B4.23 F235.23=.49:

(N )1) " (M )1) .

4$*$':+1.#&$ C-#)2"" 1->1 " 2->1 01*?')18 10"(&8:A+ 0*1- (+$%O"$ !G3, #:;&8:$,&$ F(.2-950 1-1' 0 2-1' @'+9;&'( (11+8$+(+- 8$##1.

M:) <A/:? '*1/#1-*:2"1#:<=#:? C-#)2"?, 4L (1.46) @:*:)+$*"-

;-$+(? (81"," '<',$50 ='B&350 (@'4A<350) " 274950.

R74950 4L #:;&8:A+ ;#:.$#"? z, 0*" )1+1*&@ H (z) 1):;&8:$+-

(? *:8#1% #-<A.

N<',$50 ='B&350 (@'4A<350) 4L #:;&8:A+ ;#:.$#"? z, 0*" )1+1*&@ ;#:,$#:+$<= H (z) 1):;&8:$+(? *:8#&, #-<A [1].

33

J3+=': 274.: 0 @'4A<'( #:;&8:A+ ";1/*:9$#"$ )11*'"#:+ #-- <$% ()*-91.):," W) " 01<A(18 (;8$;'1.):," *) #: )1,0<$)(#1% z-

0<1()1(+". M:) /-'$+ 01):;:#1 ((,. 00. 1.5.5–1.5.6), +:):? ):*+: ?8- <?$+(? 8$(=,: 8:9#1% >*:C".$()1% @:*:)+$*"(+")1% !G3.

1.4.3. ,E<19:5-DE> C.7./<8:K0:3 G?06I11 1 7<E0:580:H: ?7<-0.01D

F; (*:8#$#"? 0$*$':+1.#1% C-#)2"" (1.46) " (11+8$+(+8-AS$>1 $% *:;#1(+#1>1 -*:8#$#"? (1.15) <$>)1 8"'$+=, .+1:

- ,#1>1.<$# B0<40=.49 4L (8?;:# ( 1+(.$+:," 81;'$%(+8"? bi x(n ) i) ; 0*" R+1, 8$<"."#: ;:'$*9)" i 1+(.$+: x(n ) i) 1+1/*:9:-

$+(? (+$0$#=A z)i , : )1RCC"2"$#+& bi 1(+:A+(? #$";,$##&,; (",-

81<".$()" R+1 (11+8$+(+8"$ ,19#1 ;:0"(:+= (<$'-AS", 1/*:;1,: bi x(n ) i) X bi z)i , i $ 0, 1,..., N )1;

-,#1>1.<$# F235.23=.49 4L (8?;:# ( 1+(.$+:," *$:)2"" y(n)

"ak y(n ) k) , 0*" R+1, (81/1'#&% .<$# 8($>': *:8$# 1:

a0 $ 1,

+:) ):) 8 B6 1# (11+8$+(+8-$+ *$:)2"" y(n) ((,. 0. 1.4.2);

8$<"."#: ;:'$*9)" k 1+(.$+: y(n ) k) 1+1/*:9:$+(? (+$0$#=A z)k , : )1RCC"2"$#+& ak ,$#?A+ ;#:); (",81<".$()" R+1 (11+8$+(+8"$

,19#1 ;:0"(:+= (<$'-AS", 1/*:;1,:

ak y(n ) k) X )ak z)k .

B719.7 1.7. G:#: 0$*$':+1.#:? C-#)2"? 1/S$>1 8"':. U:0"(:+= (11+8$+(+8-AS$$ $% *:;#1(+#1$ -*:8#$#"$:

- '<? F(.23 1-1' @'+9;&3 (."(<"+$<= " ;#:,$#:+$<= 4L – ,#1>1-

.<$#& 1->1 01*?'):): 0$*$':+1.#1% C-#)2""

 

b

# b z)1

 

H (z) $

0

1

 

(1.47)

1 # a z)1

 

 

 

 

1

 

 

(11+8$+(+8-$+ *:;#1(+#1$ -*:8#$#"$

 

y(n) $ b0 x(n) # b1x(n )1) ) a1y(n )1) ;

(1.48)

- '<? F(.23 2-1' @'+9;&3 (."(<"+$<= " ;#:,$#:+$<= 4L – ,#1>1-

.<$#& 2->1 01*?'):):

34

0$*$':+1.#1% C-#)2""

b # b z)1

# b z)2

 

 

 

H (z) $

0 1

 

 

2

(1.49)

1# a z)1

# a

 

 

2

z)2

 

 

1

 

 

 

 

(11+8$+(+8-$+ *:;#1(+#1$ -*:8#$#"$

y(n) $ b0 x(n) # b1x(n )1) # b2 x(n ) 2) ) a1y(n )1) ) a2 y(n ) 2) . (1.50)

U8$#1 #:;&8:A+ ?&;"+7<, $(<" B0<40=.4- $>1 0$*$':+1.#1% C-#)2"" *:8$# 1.

4L /:;18&@ ;8$#=$8 1->1 " 2->1 01*?')18 ",$A+ 8"' (11+8$+(+-

8$##1:

1

 

 

1

 

 

 

H (z) $

;

H (z) $

 

 

.

1 # a z)1

1# a z)1

# a

2

z)2

 

1

 

 

1

 

 

 

1.4.4. B.7./<8:K0<D G?06I1D

1 19C?=>50<D T<7<68.715816< E-.0< 2-H: C:7D/6<

60*1S$##:? ,$+1'"): 10*$'$<$#"? ",0-<=(#1% @:*:)+$*"(+"- )" h(n) 01 ;:':##1% 0$*$':+1.#1% C-#)2"" H (z) 0*$'01<:>:$+, .+1

8;:",1(8?;= ,$9'- FN " 4L ,3F'($H ;8$#=$8 ";8$(+#: "; +:/<"2& (11+8$+(+8"% ((,. +:/<. 1.4), 8 0*$'01<19$#"", .+1:

X (z) – 0$*$':+1.#:? C-#)2"? H (z) ,3F'('1' ;8$#:; x(n) – ",0-<=(#:? @:*:)+$*"(+"): h(n) ,3F'('1' ;8$#:.

3<$'18:+$<=#1, 0$*$':+1.#1% C-#)2"" ,3F'('1' ;8$#: 1->1 01- *?'):

 

 

1

 

 

 

 

 

 

H (z) $

 

 

 

 

 

 

1 # a z)1

 

 

 

 

 

 

1

 

 

 

 

 

 

(11+8$+(+8-$+ ",0-<=(#:? @:*:)+$*"(+"):

 

 

 

 

h(n) $ ()a )n ,

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

: 0$*$':+1.#1% C-#)2"" ,3F'('1' 2->1 01*?'):

 

H (z) $

 

1

 

 

 

 

 

 

1# a z)1 # a

2

z)2

 

 

 

 

1

 

 

 

 

(11+8$+(+8-$+ ",0-<=(#:? @:*:)+$*"(+"):

 

 

 

 

h(n) $ r n

sinB(n #1)KSC

,

(1.51)

 

S

 

 

sin(KS)

 

 

 

 

 

 

 

 

 

 

 

 

>'$ rS " K S – *:'"-( " ->1< )1,0<$)(#1-(10*?9$##&@ 01<A(18

z

$ r eL jKS .

 

 

 

 

 

(1.52)

*1,2

 

 

S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35

U#:.$#"? rS " K* " a1 " a2 (8?;:#& ,$9'- (1/1% (11+#1O$#"?-

," ((,. +:/<. 1.4)

 

 

$ r 2 ;

 

 

a

2

(1.53)

 

 

S

 

a1

$ )2rS cos(KS) .

(1.54)

J:01,#", ((,. *"(. 1.11),

.+1 ->1< 01<A(: K S

$(+= #1*,"*1-

8:##:? .:(+1+: 3S .

 

 

 

 

U'$(= " 8 ':<=#$%O$, /-'$, "(01<=;18:+= "#'$)(& ;8$;'1.): " )*-91) '<? 1/1;#:.$#"? @'4A<3 " 2749 (11+8$+(+8$##1.

G<? ;:0"(" FN #$/:;181>1 ;8$#: 2->1 01*?'): '1(+:+1.#1 81(- 01<=;18:+=(? (81%(+8:," <"#$%#1(+" Z-0*$1/*:;18:#"? " +$1*$,1% 1 ;:'$*9)$.

71>': 0$*$':+1.#1% C-#)2"" #$/:;181>1 ;8$#: 2->1 01*?'):

H (z) $ b0 # b1z))1 # b2 z))2 1# a1z 1 # a2 z 2

/-'$+ (11+8$+(+818:+= ",0-<=(#:? @:*:)+$*"(+"): #$/:;181>1 ;8$#:

2->1 01*?'):

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h(n) $ b r n

sinB(n #1)KS C

# b r (n)1)

sin(nKS)

# b r (n)2)

sinB(n )1)KS C

 

 

 

 

 

 

 

 

 

 

0 S

 

 

 

sin(KS)

1 S

sin(KS)

2 S

 

 

sin(KS)

 

 

 

 

 

 

 

 

 

 

 

 

"<" ( -.$+1, #-<$8&@ #:.:<=#&@ -(<18"%

 

 

(1.55)

 

 

 

 

 

 

'b r n

sinB(n #1)KS C

 

, n $ 0;

 

 

 

 

 

 

 

 

(1.56)

 

 

 

 

 

 

 

 

 

D

0

S

sin(KS )

 

 

 

 

 

 

 

 

 

 

 

D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h(n) $ Db r n

sinB(n #1)KS C

 

# b r (n)1)

 

sin(nKS )

, n $1;

 

 

 

 

 

 

 

 

 

 

 

 

&

0

S

sin(KS )

1 S

 

sin(KS )

 

 

 

 

 

 

D

 

 

 

 

 

 

 

 

 

 

 

 

 

D

 

 

 

sinB(n #1)KS C

 

 

 

 

sin(nKS )

 

 

 

sinB(n )1)KS C

 

Db r n

 

# b r (n)1)

 

# b r

(n)2)

, n 0 2.

 

 

 

 

 

 

 

 

D

0

S

sin(KS )

1 S

 

sin(KS )

2 S

 

sin(KS )

 

%

 

 

 

 

 

 

 

 

 

 

 

1.4.5. %I.06< ?58:3K1-:581 C: C.7./<8:K0:3 G?06I11

D 0. 1.3.6 0*" 10"(:#"" !G3 81 (+.5.22': 1/<:(+" *:((,1+*$# )*"+$*"%, 01;81<?AS$% 12$#"+= -(+1%."81(+= !G3 01 $$ ",0-<=(- #1% @:*:)+$*"(+")$. D z-',43<=0, >'$ 1(#18#1% @:*:)+$*"(+")1% !G3 ?8<?$+(? 0$*$':+1.#:? C-#)2"? (z-";1/*:9$#"$ FN), (-S$(+-

36

8-$+ )*"+$*"%, 01;81<?AS"% 12$#"+= -(+1%."81(+= !G3 01 0$*$':-

+1.#1% C-#)2"", : ",$##1: ;49 ='1' B=',$ O>/ ,$43 7<=':B0(3, 2.',H';05' 0 ;'<=3='B2', B=',$ (<. @'4A<$ .. @.+.;3='B2': 672&800 +3<@'431340<- (27=+0 .;020B2'1' &+713 &'5@4.&<2': z- @4'<&'<=0

zSk

 

/ 1, k $ 1, 2,…, M )1 ,

(1.57)

 

>'$ zSk k-% 01<A( 4L (1.46).

J: 0*:)+")$ -(+1%."81(+= *$)-*("8#&@ !G3 1/&.#1 12$#"8:- A+ 01 /1<$$ -'1/#1,- )*"+$*"A (1.57) – 01<19$#"A 01<A(18 #: &3+=. #-<$% " 01<A(18.

1.4.6. *?=1 1 C:=@54

C.7./<8:K0:3 G?06I11 E-.0>.- 2-H: C:7D/6<

U8$#1 2->1 01*?'): 10"(&8:$+(? 0$*$':+1.#1% C-#)2"$% (1.47).

J:%'$, &'5@4.&<2'-<'@+9%.22$. @'4A<$ 8 8"'$

z*1,2 $ rSeL jKS ,

>'$ ;#:.$#"? *:'"-(: rS " -><: KS #: )1,0<$)(#1% z-0<1()1(+" 8&- *:9:A+(? .$*$; )1RCC"2"$#+& a1 " a2 #: 1(#18:#"" (11+#1O$#"% (1.52) " (1.53) (<$'-AS", 1/*:;1,:

 

rS $ a2 ;

 

(1.58)

 

A

a

>

 

K

$ arccos? )

1

< .

(1.59)

 

S

?

 

<

 

 

@

2r* =

 

G<? 8&."(<$#"? #-<$% 8 1/S$, (<-.:$ (<$'-$+ -,#19"+= ."(-

<"+$<= " ;#:,$#:+$<= 4L (1.47) #: z2

H (z) $ b0 z2 # b1z # b2 z2 # a1z # a2

" #:%+" )1*#" -*:8#$#"? ."(<"+$<?

b0 z2 # b1z # b2 $ 0 ,

)1+1*&$ ,1>-+ /&+= 8$S$(+8$##&," "<" )1,0<$)(#1-(10*?9$##&," (8 ;:8"(",1(+" 1+ ;#:): '"()*","#:#+:):

z

$

) b1 L b12 ) 4b0b2

$ )

b

L

b12 ) 4b0b2

.

 

1

 

W1,2

 

2b0

 

2b0

 

2b0

 

 

 

 

 

 

37

Z(<" #-<" – )1,0<$)(#1-(10*?9$##&$ z# 1,2 $ I# # jJ# ,

"@ (<$'-$+ 0*$'(+:8"+= 8 01):;:+$<=#1% C1*,$

 

 

 

 

 

 

z

# 1,2

$ r eL jK# ,

 

(1.60)

 

 

 

 

#

 

 

 

 

>'$ *:'"-( r# " ->1< K#

10*$'$<?A+(? "; (1.31) " (1.32) (11+8$+(+-

8$##1:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A J >

r $

I

2

# J 2

;

K

$ arctg?

 

#

< .

#

I

 

#

 

#

 

#

?

<

 

 

 

 

 

 

@

 

# =

Z(<" )1RCC"2"$#+ b0 $ 1, +1 8&."(<$#"$ )1,0<$)(#1-(10*?9$#- #&@ #-<$% ,19#1 -0*1(+"+=: #$ -,#19:? ."(<"+$<= " ;#:,$#:+$<=

4L (1.47) #: z2 , 10*$'$<?+= #-<" 8 8"'$ (1.60), >'$ r

" K *:((."+&-

 

 

 

 

W

W

8:A+(? 01 C1*,-<:, 01'1/#&, (1.53)–(1.54), : ",$##1:

b

$ r2 ;

b $ )2r cos(K ) .

 

2

#

1

W

W

 

1.5.%B+$)*+& 2+*&L*MP "+$#'&J*MP $+$J&N

,V)$J%J*%L %Q2)$J+

D *:;'. 1.3 *:((,:+*"8:<1(= 10"(:#"$ !G3 81 (+.5.22': 1/<:(- +": ",0-<=(#:? @:*:)+$*"(+"): " (11+#1O$#"$ 8@1'/8&@1' 8 8"'$ C1*,-<& (8$*+)" <"/1 *:;#1(+#1>1 -*:8#$#"?. U'$(= *:((,:+*"8:- $+(? "@ 1+1/*:9$#"$ 8 B3<='=2': 1/<:(+".

K0"(:#"$ !G3 8 .:(+1+#1% 1/<:(+" 01;81<?$+:

-88$(+" C-#':,$#+:<=#1$ '<? +$1*"" <"#$%#&@ ("(+$, 01#?+"$

.:(+1+#1% @:*:)+$*"(+")"; 0*" 0*1$)+"*18:#"" /1<=O"#(+8: ("(- +$, TK3 ",$##1 ) .:(+1+#&, @:*:)+$*"(+"):, 0*$'[?8<?A+(? " 8&'$*9"8:A+(? +*$/18:#"?;

-10*$'$<?+= *$:)2"A !G3 8 -(+:#18"8O$,(? *$9",$ #$ +1<=)1 #: >:*,1#".$()1$ 81;'$%(+8"$, #1 " #: <A/1$ 81;'$%(+8"$, )1+1*1$ ,19#1 0*$'(+:8"+= ):) <"#$%#-A )1,/"#:2"A >:*,1#".$()"@ 81;- '$%(+8"%.

1.5.1. V<58:80<D T<7<68.715816<. $::80:S.01. -T://-4T:/

K(#18#1% @:*:)+$*"(+")1% !G3 8 B3<='=2': 1/<:(+" ?8<?$+(? C-*=$-";1/*:9$#"$ ",0-<=(#1% @:*:)+$*"(+")" h(nT ) , )1+1*1$ 10-

*$'$<?$+(? 01 C1*,-<$ @+95'1' 0*$1/*:;18:#"? L-*=$

38

-

H (e j3T ) $ ,h(nT )e) j3Tn ,

n$0

"<" '<? #1*,"*18:##&@ .:(+1+& " 8*$,$#":

!

-

!

H (e j3) $

,h(n)e) j3n .

n$0

(1.61)

(1.62)

4*" ";8$(+#1, C-*=$-";1/*:9$#"" H (e j3T ) ",0-<=(#:? @:*:)- +$*"(+"): h(nT ) #:@1'"+(? ( 01,1S=A ',+3=2'1' 0*$1/*:;18:#"? L-*=$

 

 

2

 

 

 

 

 

 

 

 

T

 

T

h(nT ) $

 

 

Y H (e j3T )e j3Tnd3 ,

22

 

)

2

 

 

 

T

 

 

 

 

!

>'$ H (e j3T ) $ H (e j3) #:;&8:A+ &'5@4.&<2': B3<='=2': H3+3&=.-

+0<=0&': (MPN) "<" )1*1+)1 B3<='=2': H3+3&=.+0<=0&': (PN);

R+1 ,:+$,:+".$()1$ 10*$'$<$#"$ PN.

K0*$'$<", PN 01'1/#1 +1,-, ):) R+1 '$<:$+(? '<? <"#$%#&@ 3234'1'($H ("(+$,, 1+#1("+$<=#1 )1+1*&@ ";8$(+#1, .+1 >:*,1#".$- ()1$ 81;'$%(+8"$ 8&;&8:$+ >:*,1#".$()-A *$:)2"A =': %. B3<='- =$, #1 (8 1/S$, (<-.:$) '*->1% :,0<"+-'& " #:.:<=#1% C:;&.

B:((,1+*", *$:)2"A !G3 #: ;0<&+.=2'. &'5@4.&<2'. 13+5'20-

B.<&'. 81;'$%(+8"$

!

!

 

x(n) $ Cxe j3n $ Cxe jKx (3)

(1.63)

( :,0<"+-'1% " C:;1% (11+8$+(+8$##1

Cx $ const ; Kx (3) $ 3n .

G<? 8&."(<$#"? *$:)2"" 81(01<=;-$,(? C1*,-<1% (8$*+)"

(1.13)

-

-

!

!

-

!

y(n) $ ,h(m)x(n ) m) $

, h(m)Cxe j3(n)m) $ Cxe j3n ,h(m)e j3m $

m$0

m$0

-

 

m$0

 

 

 

!

 

 

$ x(n) ,h(m)e j3m ,

 

 

m$0

1+)-': ( -.$+1, 10*$'$<$#"? PN (1.62) y(n) $ x(n)H (e j3! ) .

39

y(n)

J: 1(#18:#"" R+1>1 .:(+1+#-A @:*:)+$*"(+")- ,19#1 0*$'(+:- 8"+= ):) 1+#1O$#"$

!

H (e j3 ) $ x(n) ! (1.64)

x(n)$Ce j3n

" 10*$'$<"+= (<$'-AS", 1/*:;1,.

B&01"1$"/ *&3&51.3%01%5"/ (PN) H (e j3! ) !G3 23F$(3.=<9

B3<='=239 F3(0<05'<=- '=2'P.209 +.3&800 & ;0<&+.=2'57 13+5'- 20B.<&'57 ('F;.:<=(0A ( 7<=32'(0(P.5<9 +.%05..

41'.$*)#$,, .+1 1+#1O$#"$ (1.64) (0*:8$'<"81 "()<A."+$<=#1 '<? 13+5'20B.<&'1' ('F;.:<=(09 " 7<=32'(0(P.1'<9 +.%053 *:/1+& !G3.

41?(#",, (,&(< «-(+:#18"8O$>1(? *$9",:». 7$1*$+".$()", 1/- <:(+= ";,$#$#"? >:*,1#".$()1>1 81;'$%(+8"? ) - / n / - . K'#:)1 #: 0*:)+")$ ",$A+ '$<1 ( -(<18#1 >:*,1#".$()", 81;'$%(+8"$, 8 1/<:(+" 0 " n / - , >'$ 8*$,? n $ 0 (11+8$+(+8-A+ #:.:<- 81;'$%(+- 8"?. D +$.$#"$ 8*$,$#" 0 " n / n0 !G3 *:/1+:$+ 8 *$9",$ 0$*$@1'- #&@ )1<$/:#"%. 30-(+? 8*$,? n0 0*12$(( -(+:#:8<"8:$+(? " *$:)2"?

(+:#18"+(? 0$*"1'".$()", (">#:<1,, 01R+1,- 8 ':##1, (<-.:$ ",$- $+ (,&(< >181*"+= 1 *$:)2"" ):) 1 >:*,1#".$()1, (">#:<$ 8 -(+:#1- 8"8O$,(? *$9",$.

M1,0<$)(#-A C-#)2"A H (e j3! ) ,19#1 8&*:;"+= .$*$; $$ ,1- '-<= " :*>-,$#+:

!

 

!

 

e j argEH (e

!

 

 

 

 

j3

 

!

 

 

 

H (e j3 ) $

 

H (e j3 )

 

 

)F $ A(3)e

H1'-<= .:(+1+#1% @:*:)+$*"(+")"

!

H (e j3 )

=7;2'-B3<='=2': H3+3&=.+0<=0&': (EPN)

 

!

 

 

!

 

,

 

 

 

 

 

 

 

 

 

A(3) $

 

 

 

H (e j3 )

 

 

 

!

jK(3) .

#:;&8:A+

(1.65)

35@40-

(1.66)

: :*>-,$#+63F'B3<='=2': H3+3&=.+0<=0&': (LPN) !G3

 

!

!

(1.67)

K(3) $ argEH (e j3 )F.

41?(#", (,&(< EPN " LPN, '<? .$>1 0$*$0"O$, 8&*:9$#"$ '<? *$:)2"", 01'(+:8"8 8 #$>1 81;'$%(+8"$ (1.63) " PN (1.65):

40

Соседние файлы в предмете Цифровая обработка сигналов