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.

1.

1.1. ⠠

1.2. ' ⠠

1.3. '

1.4. Z -

1.5. Z -

1.6. '

2.

2.1. 㠠

2.2. ࠠ

2.3.

2.4. 蠠

2.5. . .

2.6. ࠠ

2.7. . 𠠠

2.8. 㳿 ࠠ

2.9. 堠

3.

3.1. ⠠

3.2. 󠠠

3.3.

3.4.

3.5. . .

3.6. 蠠

3.7. .

4. .

4.1.

4.2.

4.3.

4.4. . .

4.5.

4.6. 󠠠

4.7. Ԡ

4.8. 蠠

5. ³

5.1. Ϡ

5.2.

˳

. . , .

. .

.

 

1. .

1.1 .

X(t) ,

x(nT) , x(n) , xn , {x0 ; x1 ; x2 ; } .

() T (. 1.1).

X(t) X(nT). f T '

f = 1 / T . (1.1)

()

x(nT) = x(t)d(t - nT) , (1.2)

d(t) - d - (. 1.2, ),

d(t - nT) - d - (. 1.2, ).

, , .

1.2. ' .

(1.2)

X(jw) =x(nT) e-jwt dt =x(t)d(t - nT) e-jwt dt .

d - '

d(t - nT) =,

'

, Fd(jw) = 1

ϳ d - '

X(jw) =x(t)() e-jwt dt =x(t)e-jwt dt .

, . :

f(t) F(jw), f(t) F[j(w w0)] ,

, ' X(jw) Xa(jw)

X(jw) =Xa[j(w -)] . (1.3)

(1.3) 1.3, , :

1. , w

2. [-0,5w ; 0,5w],

w 0,5w , (1.4)

w - .

г (1.4) w.

1. Xa(jw) (1.3) , (1.4) ( 1.3, ). . ֳ .

2. , w = 0,5w. . , (1.4). , .

(1.4). w , w (1.1), T , ' .

1.3 ' .

' . ,

'

', 䳿 .

' , X(nT) X(nT) / T '

(1.5)

(1.5) , jw P = d + jw

(1.6)

1.4. Z - .

, Z - . X(p), P = d + jw, Z - X(Z), Z = x + jy.

Z - (1.6)

epT = Z . (1.7)

(1.7)

dZ / dp = TepT

(1.6) Z -

(1.8)

p = d +jw, p = jw, . Z , (1.7)

Z = ejwT = (1.9)

p = d + jw, z = x + jy (. 1.4). , , , z - (1.8) z p.

(1.7), (1.9) , p = d + jw z = x + jy, - z .

(1.9) z - , (1.7) .

. x(nT) = {a ; b} (. 1.5, ).

г.

Z - (1.8)

X(Z) =x(nT) Z-n = x(0T) Z-0 + x(1T) Z-1 = a + bZ-1

(1.9)

X(jw) = a + be-jwT.

1.6, , [0 ; w].

[0 ; w] w.

1.5 Z - .

z - , .

1. .

x(nT) = ax1(nT) + bx2(nT) ,

X(Z) = a X1(Z) + bX2(Z).

2. .

x(nT) = x1(nT - QT) ,

X(Z) = X1(Z) Z-Q.

3. .

X(nT) = x1(kT) x2(nT - kT) ,

X(Z) = X1(Z) X2(Z).

4. .

x(nT) = x1(nT) x2(nT) ,

X(Z) = X1(V) X2() V-1 dV,

V, Z - Z.

5. ( ).

x2(nT) =X(Z) X(Z-1) Z-1 dZ.

Z - .

1.6. '.

tu , - w , N , (. 1.7, , ) :

N = tu/T - , T = 1/f ,

N = f/f1 - , f1 = 1/tu .

, . X(nT) = {X0 ; X1 ; XN-1} ' X(jkw1), , w. ³, X(jkw1) = {X0 ; X1 ; XN-1} ' X(nT), , tu.

' ' (). ' (1.5), w kw1,

w kw1 , dw w1.

ϳ (1.5)

X(jkw1) = x(nT),

x(nT) =X(jkw1).

w1 = w/N, T = 2p/w

X(jkw1) =x(nT)- ,

x(nT) =X(jkw1)- (1.10)

, , , . , N. (1.10) ' N N , .

. . 1.5, .

N = 2 X(jkw1) =x(nT) e-jpkn

X(j0w1) =x(nT)e-j0 = x(0T) + x(1T) = a + b

X(j1w1) =x(nT)e-jpn = x(0T) e-j0 + x(1T) e-jp = a - b

. 1.5, , w1 = w/N = 0,5w.

N , : kw1 . ³ , N. , 㳺 , , , .

. X(t) = Ae-at = 1 e-10t .

г.

X(t) . 1.8

T = 0,02. ' ( . 1.8) t = 0, .

tu = 0,4.

N = tu/T = 20.

w = 0 (k = 0)

X(j0w1) = 1,0 + 0,8187 + 0,6703 + 05488 + 0,4493 + 0,368 + 0,3012 + 0,2466 + 0,2019 + 0,1653 + 0,1353 + 0,1108 + 0,09072 + 0,07427 + 0,06081 + 0,04979 + 0,04076 + 0,03337 + 0,02732 + 0,02237 = 5,41

w = 0

Xa(jw) =, Xa(j0) == 0,1.

, T, ' .

X(jow1) = 5,41 T = 5,420,02 = 0,1082.

Xa(jw) X(jw) w = 0 . .

, X(t). t = 0.

, , , . ' (), . , .

2.   .

2.1 .

x(t) y(t) ' . t nT . , , ',

y(nT) =am x(nT - mT) +y(nT -), (2.1)

(M + 1) - ',

Z - ',

m, , n - .

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