MTMO / Приставка О.П., Приставка П.О., Ємел'яненко Т.Г., Мацуга О.М. Випадков_ процеси (correct)

x i(S2,0 (S2,0 ))

i+ 2

x i(S3,0 (S3,0 ))

i+2

γ 1,(Sj2,0 (S2,0 ))xj ,

= γ 1,(Sj3,0 (S3,0 ))xj ,

j=i−2

j=i−2

x i(S4,0 (S4,0 )) =

i+ 4

γ 1,(Sj4,0 (S4,0 ))xj ,

j=i−4

−1

−152

−1

−1

−6236

−12

−8

−35112

γ (S2,0 (S2,0 ))

=

1

26

;γ (S3,0

(S3,0 ))

=

1

18

; γ (S4,0 (S4,0 ))

=

1

83002

.

1

64

1

36

1

147456

−12

−8

−35112

−1

−1

−6236

−152

−1

γ

(Sr,0 (Sr,0 ))

γ

(Sr,0 )

1

2

(Sr,0 (Sr,0 ))

n

(Sr,0 )

(Sr,0 )

=

γ 1,i (n− j)

γ 2,k,k +(n− j)

,

j = 1,n ,

n = rg

γ 2

,

k =1

h

(2.22)–(2.23).

# ,

,

h ( (2.25).

,

( ) ( S2,0 ( . 2.8, ), S4,0

( . 2.8, ).

, ".

$

" .

1. )

#

(0;B)

*

(B;F ) *.

3. )

( fc − B 2; fc + B 2) *.

4. )

"

( fc − B 2; fc + B 2)

*,

.

' . 3.1 "

( , & #).

'

",

"

N → ∞ ,

&

,

.

) " .

+

"

.

M

yi = ck xi−k .

k=−M

, &

, ck = c−k , #

%’# ' −π ≤ ω ≤ π ,

ω –

. +

f

'

−1 2 ≤ f ≤ 1 2 .

H ( f )

f = 0. )

-

.

- .

x(t) "

xi ,

&

'. 3.2. 0$ x(t) = −t + round (t) '$#& $ &

" * . 0 1"+ +’! +$, 1

& , , ' 0 .$, k = 10 ( )

k = 50 ( )

1 *, " , ,

2, " # - .

&

H ( f ) , :

−

M # %’#;

−

" # -

σ (M ,k) =

sin(πk M )

,

πk M

" M ;

− #

ck

2 ( ).

'

#

H ( f ) = 1,

0 <

f

< 0,2,

0,2 <

< 0,5,

0,

f

4

∞

sin(4kπ 10)

H ( f ) =

+ 2

cos(2πkf ).

10

k =1

πk

4

4

sin(4kπ 10)

H ( f ) =

+ 2

cos(2πkf ).

10

k =1

πk

σ (5,k) =

sin(πk 5)

.

πk 5

σ (5,5) = 0

a5

#.

#

4

4

sin(4kπ 10)

sin(kπ 5)

H ( f ) =

+ 2

cos(2πkf ).

10

k =1

πk

kπ 5

,

"

M

M

Y ( f ) = X ( f ) bk exp(− j2πfkT )− Y( f ) am exp(− j2πfmT ),

k=0

m=1

M

Y ( f )

bk exp(− j2πfkT )

H ( f ) =

=

k=0

,

X ( f )

M

1+ am exp(− j2πfkT )

3 D( f ) = 0

# f1,..., fM ,

D( f ) "

M

D( f ) = a0∏(1− exp(− j2πT ( f − fk ))),

k=1

a0 – ".

. D( f ) .

1. 4 . + fk

jαk

jαk

+ F ,

2πT

2πT

αk > 0.

$ "

jα

k

(1

− exp(−αk )z−1).

1

− exp

− j2πT

f

−

=

2πT

, & #

jαk

+ F ,

(1+ exp(−αk )z−1)

2πT

.

2. . . + # -".

, &

f

k

=

jαk + βk

,

2πT

βk > 0, k′ ,

fk′ =

jαk − βk

.

2πT

"

jα

k

+ β

k

jα

k

− β

k

1− exp − j2πT f

−

1− exp − j2πT f

−

=

2πT

2πT

P

Q 2

D( f ) = ∏(1− α1pz−1)∏(1− α1qz−1 − α2qz−2 ),

p=1

q=1

α1p ,α1q,α2q

– .

( #, & D( f )

" "

"

#.

, &

,

H ( f ) =

b0

.

D( f )

$ Hr ( f )

b1 R

0

,

z−1

1− α

Hr ( f ) =

1p

b1 R

0

,

1− α1qz−1 − α2qz−2

R = P + Q 2;

r = q = 1,...,Q 2 ; p = r − Q 2,...,R .

R

H ( f ) = ∏Hr ( f ).

r=1

! Hr ( f ) –

,

&

, "

.

# #.

3.1.

5-

"

.

3 r -

#

u(r)

= b′ u(r−1)

− α

u(r)

− α

2r

u(r)

,

i

0

i

1r i−1

i−2

b′

= b1 R ;

u(0) = x ;

u( R)

= y .

0

0

i

i

i

i

r -

u(r−1)

, – u(r) .

i

i

3

. )

"

. +

#

f . ,

"

5:

H ( f )

2 =

1

,

sin(πfT ) 2M

1+

sin

(πBT )

H ( f )

2 =

1

.

tg

(πfT ) 2M

1+

tg (πBT )

+

1,

f = 0,

H ( f )

2 = 1 2,

f = B,

f > B.

< 1 2,

. ' – # am

bk

#, & #

.

$+'$ -

$& , (

) ' 2 # + .

.

H ( f )

2 =

1

.

sin(πfT ) 2M

1+

sin(πBT )

1.

$

’

sin(πfT ) 2M

D(

f ) = 1+

= 0.

sin(πBT )

2.

) 2M M , M –

.

$

&, .

3.

$ ’ αm βm

β

m

+ jα

m

sin

= am + jbm .

2

4.

"

(αm,βm ),m = 1,...,M

a1m = 2exp(−αm )cosβm ,

a2m = − exp(−2αm ),

m = 1,...,M 2

M – .

+

M

m = 1,...,(M −1) 2

2.

!

fact = sin(πBT )

:

sector = π M ,

wedge = sector 2 ,

fn = 0,

F = 1,

m = 1.

3.

!

fn = m −1,

U = fact sin( fn sector + wedge),

C = 1− fact2 ,

D =

−C +

C2 + 4U 2

,

2

2(2U 2

D −1)

E = D + 1 + D ,

G =

,

E2

H = −E−4 ,

F = F (1− G − H ).

4.

! #

a1,m = −G ,

a2,m = −H .

5.

- m

1:

m = m + 1.

, &

m ≤ [M 2],

3, – 6.

6.

, & M ,

m = (M + 1)

2 a1,

(

M +1 2 ,

a2,

(

M +1 2

)

)