ЦСАУ

51

3 Z-

, -

( ) ,

z- . z-

, -

.

–

, z- -

-

.

3.1

3.1.1 z-

« -

», z-

eTs = z. –

s, -

, (2.23) (2.28) « » -

-

z.

, (2.23), (2.28) (2.25)

z- :

F (z) f (kT )z k ,

k 0

k

N ( n )

1

F ( z ) F ( s )

1

,

n T

s

ln z

n 1

D ( n ) 1

z

1

e

T

1

F ( z )

F ( s jn s )

s

1

ln z ,

T

n

T

F ( ) N ( ) , n – F( ).

D( )

(3.1)

(3.2)

(3.3)

52

,

(3.1) .

(3.1) , z- -

z.

(3.2) (3.3) ,

, (2.28) (2.25).

(3.1)–(3.3), z-

, -

, z- -

.

z- , -

, F(z)=Z{f(t)},

F(z)=Z{F(s)}.

, z-

, F(s).

3.1. z-

1(t). (3.1),

Z 1(t) 1(kT )z k	z k .						z		1.
k 0	k 0
( ):
		1		z
	z k				.
		1 z 1
	k 0			z 1

eTs z -

, 2.1 2.2. , -

:

1				1		z
Z 1(t) Z								.
						z 1
s		1 z 1

3.1.2 s- z-

s- z- -. , -

. z-

53

-

, , .

, -

F(s), , -

f(t). F(s) -,

	Im s i			s	,	(3.4)
			2
F*(s)						-

, -

-

. z- , z = eTs,

,

F*(s), , -

z = eTs -

z,

. , z- F(z)

(3.4) -

f(t).

(3.4) , F(s)

, ,

F*(s) -

, ,

F(s), (

), -

z F(z).

f(t) F(z) ,

« » F(z).

, ,

, (3.4) (2.31).

s-

-

( , , ,

, .). ,

z- .

, s-

.

54

, 1-2-3-4-5-6 3.1 -

z = eTs

. 3.2).

Im s

s/2

3	2
	1
	6	Re s
	5

4

– s/2

3.1

Im z

2	3	1	Re z
5	4	6

3.2

e(s jm s )T esT ejnm esT z ,

s -

. , s

z, -

s- ,

.

55

, s -

s = +j ( = const), z = eTs -

e T, -– s/2 + s/2 z -

( -

3.3). s -

s = j ) , -

3.3 .

		Im s
		s/2							Re s
– 2								1
		– s/2
		a)
		Im z

e–	T Re z
T	e 1

)

3.3

s = + j ( = const)

s ,

T. , z:

z

Ts

T

e

jT

T

Re z

jIm z.

(3.5)

e

e

e

(cos T

j sin T )

56

Re z Im z z,

(3.5), :

Imz Re z tg T,

(3.6)

T ( .

3.4).

Im s

s/2

2

1

Re s

– 1

– 2

– s/2

a)

Im z

2T 1T

– 1T Re z

– 2T

)

3.4

57

s -

z, s/2 – -

.

3.1.3 z-

z-

, , -

-

.

1.z- , -

– , -

.

-

.

2.z- Y(z) – -

y(t) -

. , Y(z)

y(t) . ,

Y(z) –

) y(kT) y(t)

t = kT.

3.z-

-

, .

–

) t = 0.

, z- , -

. , , -

.

.

z- , -

. (

) -

z- .

58

3.2

3.2.1

-

z- .

r(t)

( 3.5). « »

, , W(s)= = (s)/R (s).

r(t)				y(t)
			W(s)	(s)
R(s)

3.5

:

r*(t) r(t) (t-kT ).

k 0

(s) =R*(s) W(s), R*(s) – -

.

z- , (2.25):

*	1			1			*
(s)		(s jn s )				R (s jn s ) W(s jn s ). (3.7)
	T n			T n
R*(s+jn s)= =R*(s), (3.7) :
		*(s) R*(s) W (s jn s ).								(3.8)
:					n
					W (s jn
		W * (s)	1						),	(3.9)
		T n						s

59

(3.8) :

*(s) =R*(s) W*(s), (3.10)

, z = eTz, :

(z) =R(z) W(z). (3.11)

W(z) -

. (3.11),

z- z-

( -) , (3.9),

:

		1
	W (z)		W (s jn s )		s	1	ln z .	(3.12)
	T n				T

y(t) , -

(3.11) -

.

(3.11) -

.

, -

t = 0 ( 3.6).

					S2	*	(t)
						y
r(t)	S1		r*(t)			*(s)
				W(s)		y(t)
R(s)			R*(s)			(s)

3.6

-

w(t).

S2, 3.6 ,

:

y* (t) w* (t) w(kT ) (t kT ) ,	(3.13)

k0

w(kT) –

k = 0, 1, 2,…

60

:

r*(t) r(kT) (t kT) .

	k 0
:
y(t) r(0) w(t) r(T)w(t T) r(2T) w(t 2T) ...			(3.14)
t = kT (k N0) (3.14) :
y(kT ) r(0) w(kT ) r(T ) w (k 1)T ... r(kT ) w(0)
k			(3.15)
r(nT ) w (k n)T .
n 0
:
	k
y*(t) y(kT) (t kT) r(nT) w((k n)T) (t kT) . (3.16)
k 0	k 0 n 0

z- . -

z- (3.15),

, -

z = eTs -

(3.16).

( (3.11)):

(z) =R(z) ·W(z).

W(z) z- w(t):

W (z) w(kT )z k	(3.17)

k 0

, (3.11), z-

.

, (3.11) z -

(z) y(t)

.

.

, y(t)

, z-

.