-
:
::. - . -
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1.21.1 22. 62.1 62.2 62.3 93. 143.1 143.2 153.3 363.3.1 1:
363.3.2 2: 384.BIBO 394.1 415. :43
1. . . . . ( ) . ( ) ( ). . - . , .
1.1 , : . , . , . ( ), (), ( ).
. . , : s (x, t) ( ). , , 0. 1.1 ( 1.1). , . - , . 1.2, . . , ..
, , . , , , : , . , : s (x) = (r (x) , g (x) , b (x))T . , , . , ,
.
1.1: . ( )
. ( , ).
Ascii
1.3: ASCII . .. 7- ( ?); ASCII 8- . (-16). , .
, . , . ASCII , , - . , ASCII 97 65. 1.3 .
2.
2.1 , . . , , , (DSP). , . , , .. .
2.2
, . , - - . , .
() (), . H (kf (t)) = kH (f (t))
2.1:
2.2: H (f1 (t) + f2 (t)) = H (f1 (t)) + H (f2 (t)) (2.2) () . ,
:H (k1f1 (t) + k2f2 (t)) = k2H (f1 (t)) + k2H (f2 (t)) (2.3)
: . H (f (t)) = y (t), H
H (f (t T)) = y (t T) (2.4)
2.3: . .
, , .
; , . , . ; , , . . () , .
. . , , x (t) y (t) |y (t) | _ My < 1 (2.5) |x (t) | _ Mx
< 1 (2.6)
Mx My t. , .. ( ) , .
2.3
, , , , , .
2.4: ) ... ) ... t0, y (t0), t0.
2.5 () , L y , () . . , . () , () . . , x y , .
, .
2.8: () t () , 10 . , , , .. () 10 .
, x(t) x(t t0) TI. , x(t) x(t t0) . x(t t0) t0. , . . , .
(LTI) LTI . LTI , . .
2.6: () , () . .
2.7: () , () .
2.9: . () , (), .
2.10: LTI
LTI LTI , . .
LTI LTI , .
, . t0 , . : h(t) t t1 > 1. . t1 .
, . . , f(t) t1 > 1 t2 < 1. . , f(t) :
2.21: () ()
. , , . , . . , . . , . , , . , . , , . , . , : . , , .
2.22: . .
s (n), n = {. . . ,1, 0, 1, . . . }. . . n=m.
2.23: .
2.24:
. (2.9) . f . . (2.10)
, : (2.11) , 2.23, . s(m) m (n-m), .
(2.12) . . . , .. , , , . , , .. .
. , . {a1, . . . , aK}, . , , , . , , . , , , .
. , .
. , :
(2.13) , w , . wt . , , , :
(2.14)
2.25: =2, w=2 =0
, :
f(t)= (2.15) , :s= , :(f(t)= (2.16) . , . - , < 0 - , >
0
. , , , , t=0. , (t)
2.26: () ()
:
(2.17)
- - , :
(2.18) , , . . , , .
. : (2.19)
2.27: () ()
2.28:
: , , . : , : (2.20)(2.21) . , : . (2.22)
e , (2.23) , t , , = jw. , : (2.24)
, . , . , , . , , , = +jw, : (2.25) : (2.26) , , :. (2.27) :
(2.28) (2.29)
, . , : (2.30) nT .
, : (2.31)(2.32) (2.33)
2.29: . , t=0. () , . () , . () , .
1 -1. , . /, w .
2.30: - . , , .
(- )
s(n) n0 s ( n - n0 ), n - > 0. , . , :
: (2.34) , . S (x (n)) = y (n), S (x (n- n0)) = y (n- no).
, . , . (2.36), y (n) y (n l), l = {1, . . . , p}, x (n). q . ,
, . , , . . MATLAB 1000 :
y(0), y(-1), ..., . , . , . , : . , . : . : .
, . , . .
, , . , , . . , , 1. (2.41) (t).
2.34: .
2.35: , . , . .
. (2.42)
= 2.43) . (t - T) (t), f(t) . , . , . , .
. . u(t) .
( )
2.36:
(2.44) k s [k] k [n k], , . (2.45) .: 2.45 .
LTI , . . : (t) [n] .
3.3
. , . ? ? : , MATLAB. , .
2.31 1: p = 1 q = 0.y(n) = ay (n-1) +bx (n)(2.37) , y (n 1) . :
x (n) = (n). , n=0. y(0) = ay (-1) +b(2.38) y(-1)? , . , y (1) = 0,
y (0) = b. y(n)= ay (n-1) + b (n)(2.39) . b , . , b. , , , . , . 1,
. =1, . , -1, . =1, , b b. |a| > 1, , , .
2.32: , .
, . , n . , . 1, , 1 . . , n (, .), 1, b=1. , . , |a| = 1 b
.
2:
y (n + 1) x (n + 1), . ? .. ?: , . , .
2.3: . :(2.40) , 1q n = {0, . . . , q 1}, .
2.33: . , . 2.33 q 1q. . , q . (q=7).
4. BIBO BIBO , . BIBO . , . , . , .
2.37:
, . , . LTI h(t) BIBO , (2.46)
, h (n), . : (2.47)
4.1 . jw . .
2.38: () - . () - .
- - , . , jw , .
2.39: 9) ()
5. :[1] "Fundamentals Of Control Theory (Ch12 Of Mems
Handbook)", Bill GoodwineUniversity of Notre Dame.[2] "Signals and
Systems", Richard Baraniuk.
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