ЦСАУ

41

. ,

, F*(s)

j s. -

. , (2.23)

F*(s) m = = 1, 2, …

F*(s jm s ) f (kT)e kT(s jm s )

k 0

f (kT)e kTs e jkm2 F*(s),

k 0

f (kT)e kTs e jkm sT k 0

e–jkm2 =1 k m. F*(j )

, F*(j ) ,

s, , ( ) F*(j ),

, . -

,

+ k s (k = 1, 2 …).

F*(s) . 1. s =s1

s F*(s) s = s1+ jm s, s- :

Im s < < s/2

s/2 < Im s < 3/2 s; –3/2 s < Im s < –1/2 s; 3/2 s < Im s < 5/2 s

. ( . 2.9).

S– .

3/2 s

s/2

– s/2

–3/2 s

2.9

42

2. F(s) s = s1, F*(s) -

s = s1 +jm s m.

2.3

–

.

, -

. -

, -

, -

. -

-

, , . -

.

, -

f(0), f(T), f(2T),… -

f(kT) t = kT

f(t). -

.

2.3.1

: -

, , , -

, – .

.

2.1.

c, ,

, 2 c.

: -

, 2 c,

, .

, c,

f(n)(kT), f(n–1)(kT),… f(1)(kT), f(kT) (k = 0,1,2…), -

:

43

	T	1		(n 1)	2	,	f (i) (kT)	di f (t)			t kT .
		2						i
								dt
					c

:

:

		Sin s (t kT ) / 2
	f (t) f (kT )		,	(2.32)
		s (t kT ) / 2
	k

s, , – .

. f(t) – F(j ) –

– :

F ( j ) f (t)e j t dt ,

(2.33)

		1
	f (t)		F ( j )e j t d .
		2

. (2.30), :

	F*( j )	1		F( j jn	).
	T n			s

, ,

:

	C e jkT	,	(2.34)
F*( j )
k	k

k

:

		s
	1			2
Ck				e jk T F * ( j )d .				(2.35)
	s				s
				2

( ,

(2.31)). -

,

, .:

	44
										s
TF * ( j ),											;
					2								(2.36)
F ( j )									s
0,												.
		2

(2.36), (2.35) F*(j ) (2.36) ( -

> s/2 -

). :

Ck	1		e jk T F ( j )d	1	e jk T F ( j )d .	(2.37)
T s				2

(2.37) (2.33),

,

, = f(kT). -

(2.34) F*(j ). , ( (2.36)),

F(j ), -

( (2.33)) -

f(t).

f(kT) f(t), -

.

(2.32)

(2.33) : F(j ) c (2.36) -F*(j ). (2.34) ,

= f(kT), ,

, , ,

. .

						s						s
		1		T			2			T			2
	f (t)		F( j )e j td				F*( j )e j td						e j t			f (kT) e jk Td
		2
				2						2						k
							s						s
						2						2

45

s

s

2

T

2

T

f (kT)

e j t jk Td f (kT)

e jkt jk T

2 ( jt jkT)

k

2

k

s

2

s

Sin s

(t kT)/ 2

2

f (kT)

.

s(t kT)/ 2

k

N = s/2 -

.

2.3.2

-

(2.32). ,

, .

(2.32) ,

. (2.32) -

, t -

, -

.

, , -

, , ,

(2.32).

-

, -

, , -

.

, , -

, , -

2.10, -

. , -

46

, -

.

n(j )

1

– s/2	s/2
	2.10

, ,

,

:

) , ( > c

;) (2.31), : -

c N.

(2.31),

. -

-

.

2.3.3

– -

f(t). -

,

.

,

– -. f(t) kT t < (k + 1)T.

47

f k (t )

f (kT ) f (kT )(t kT )

f (kT )

(t kT ) 2 ..., (2.38)

2!

fk (t) f (t)

kT t (k 1)T ;

df (t)

f (kT )

t kT ,

dt

df (t)

f (kT )

dt

t kT .

:

1

f

(kT) f ((k 1)T ) ,

f (kT)

T

(2.39)

1

1

f

1)T ) f ((k 2)T )

f (kT) T

(kT)

f ((k 1)T ) T 2 f (kT) 2 f ((k

.

(2.39) , -

( (2.38)) -

f(t), -

f(kT). ,

, f(t).

(2.38) ,

( ) , ,

, -

. -

. -

.

.

1.-

.

2.– -

, -

.

, , -

:

48

e0	max	f (( k 1)T ) f (kT )	T max	f (t )	.	(2.40)
	k

. -

:

x*(t) x(kT) (t kT),

k 0

:

X * (s)

x(kT )e kTs .

k 0

:

y(t) x(kT )(1(t kT ) 1(t kT T )) .

k 0

y(t) :

kTs

e

k(T

1)s

kTs

1

e

Ts

e

Y (s) x(kT)

x(kT)e

s

s

s

k 0

k 0

X *(s)1 e Ts . s

:

W (s)	Y(s)		1 e Ts
				.	(2.41)
0	X * (s)		s

(2.41) s =

:

		1		e j T		sin		T
W0	( j )				T				2
				j		T
								2

j , -

e j T / 2 2 sin								e		j s . (2.42)
					s
	s
				s

A0( ) 0( ) -

(2.42) 2.11.

( ) -

(

2.10).

49

A0( )

2 / s

s/2

s

2 s

3 s

0( )

–

–2

–3

2.11

,

(2.38), , -

:

fk (t) f (kT) f (kT)(t kT) kT t (k 1)T . (2.43)

(

, ) :

W	(s)	eTs e Ts 2	.	(2.44)
1		Ts 2

:

e1
	max max fk (t)
	k	t

	f ( T )	t T
			( f ( T ) f ( 1)T ) .
		T

50

f(t) , :

e1	T 2 max f (t ) .
	t

,

.

,

.

2.2.1

. ,

, -.

-

.

-

.

c ( -

) ,

-

2 c. ,

.

,

, ,

, ,

, ,

-

.