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???? (sampling theorem)

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Title: ???? (sampling theorem)


1
??????? ????
2
??
  • ??
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???????
  • ???????

3
??
  • ??
  • ????(sampling)?????(uniform sampling)
  • ??????
  • ????(sampling theorem)?? ???????
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???????
  • ???????

4
????(Sampling)
  • ???????(continuous-time)?????????(discrete-time)
    ?? ????
  • ???(sample value)????????????????
  • ??????????? ,? ?????? ?????
  • ????(uniform sampling) ???????????????
  • ???????????T,?? ????????????
  • ????
  • -????????????

5
??????
  • ????,?????????????????,???????????????VLSI???,????
    ??????????????,???????????????????,???????????????
    ???

6
????(Sampling Theorem)??
  • ???????,???????????????????
  • ?? ?????????????????????,???
  • ????????????

7
????(Sampling Theorem)??(?)
??
  • ??????????????
  • ???????????,???
  • ????????
  • ?0.05???????????
  • ?????????????

8
????(Sampling Theorem)??(?)
  • ???????,???????????, ??? ???????,???????????
    ?
  • ??????? ??????????? ?
  • ?????,????????
  • ?????? ?? ?


????????????
9
??
  • ??
  • ???? (sampling theorem)
  • ?????(impulse train sampling)?????
  • ??????????
  • ??????????
  • ???????
  • ????????p(t)??????
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???????
  • ???????

10
????
  • ???????(band-limited)??? ,??????(?
    )?
  • ????? ?? ?2?,? ??????
    ?????
  • - T
    ????(????????)
  • -
    ????(?? Hz)
  • -
    ????(?? rad/sec)
  • ???????????

11
?????(Impulse Train Sampling)?????
  • ?????????????,???????????????
  • ??????
  • ???????????

????(sampling function)
12
??????????
  • ????? ??????(sampling function)
  • ? ?????
  • ??
  • ??? ??????
  • ??

?????
??????
13
??????????(?)
  • ??? ?????? ????
  • ??
  • ???????? ??????

F.T.
???????
  • ?????????? ??
  • ?????????????????????

14
????????
  • ? ,??
  • ????????????????????,???? ?????????????

???????
???????(??????????)
????????????
15
????????(?)
  • ? ,??
  • ???????????????,???????(Aliasing Effect)?
  • ???????????????????????
  • ????????(Nyquist rate)?
  • ????????????????(? ??????), ????
  • ???,?????????????

????,??????????
16
???????
  • ?????????????44.1 kHz?????,?????????
  • ? ??????????????20
    Hz20 kHz?????
  • 44.1 kHz????????????
  • ??????????????300 Hz lt4 kHz??????????
  • ????8 kHz,???????

17
????????p(t)??????
  • ????
  • ????? ??????

18
????????p(t)?????? (?)
  • ????? ??????

?????
19
??
  • ??
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ????????????
  • ????????????
  • ???? (signal reconstruction)
  • ???????
  • ???????

20
??????????????
  • ??????? rad/sec

??????

???????

21
??????????????
??
???
??
  • ????? ?

??
?? ? ???????,??????,?????? ? ?
(1)
(2)
? ??,??????????????
22
??
  • ??
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???(interpolation)???
  • ?? ?sinc???????
  • ???????
  • ???????

23
????????(Interpolation)???
  • ????????

??????????
???
????
24
???????????(?)
  • ??? h(t) ??????????

, ?????
??????x(t)
?sinc?????
?????
???
x(t)??????
?????,? ????????
25
??
  • ??
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???????
  • ?? ???????-????(Zero-Order Hold)
  • ?????????
  • ?? ???????-????(Natural Sampling)
  • ??????? I??????
  • ??????? II????????
  • ???????

26
???????-????(Zero-Order Hold)
  • ?????

????
??????????
????? ????
27
???????-????(Zero-Order Hold)
  • ?????
  • ??

28
?????????
  • ??????????(? ),
    ?????
  • ? ?

????
???????????
???????
ho(t) ? hr(t)???????
?
29
?????????(?)
?
?
?????????
????????
?
?????
30
???????-????(Natural Sampling)
  • ????????A????Tp????T????? k(t),?????
  • ???????????

????
?????? k(t)
31
???????-????(?)
  • ??????????xk(t)?????,?????

??????????????? xk(t)
32
???????-????(?)
  • ??????
  • ???????? ????
  • ???????????????????????????

33
???????-????(?)
  • ???????????????????????????????,??????????????????
    ????????

???????????
????????????????? ( )
34
???????-???? (??)
(????????)
(??????)
35
??????? I??????
  • ?????????????
  • ????????????,???????????
  • ??????

??????????
gt2w
????????,???????? ?,??????????????? ???????
2w
36
???????II????????
  • ????????????(time-limited)??,??????(band-limited)
  • ???,????????????
  • ????????,????????(anti-aliasing filter)
  • ??????fgtfs/2????(??????fs/2)?

??????
37
??????????????
???????
????????
????????
??????? ??????
?????
????????????, ??????????
??????????????
????????,?????
38
?????????????
39
??
  • ??
  • ???? (sampling theorem)
  • ??(aliasing)??
  • ???? (signal reconstruction)
  • ???????
  • ???????
  • ????????????????

40
????????????????
  • ??????,??????????,??????????
  • ???????,?????
  • ????????? ???????? ?
  • ????????????,?????????(VLSI) ?
  • VLSI????,???????????????????
  • ?,??????????????????

????
????
41
???????(CD)????
???????
??????
???????
  • ?????
  • ???? ??????? ,?????
  • ?44.1 kHz?
  • ????????????????(? Reed-
  • Solomon Codes),??????? ,???
  • CD??
  • ???
  • ? ?CD??,?????????????
  • ?????? ???(????)???

42
??
43
???
  • ??????? ???????? ???????
  • ????,?? ???????,????????????
  • ????????????????????
  • (a) ? (b)
    ? (c) ?

44
???
  • ?????W????? ,??????T?????????????
  • ??
    ,?? ????????
  • ?????????


45
???
  • ?? ??????????????,?????????
  • ? ? ???????,???? T0.2 ?????
  • (a) ???????????????
  • (b) ?? ???????? ,?????T ?????
  • ???,????? ?????????

46
????
  • OWN A. V. Oppenheim, A. S. Willsky, and S. H.
    Nawab, Signals and Systems, 2nd ed.,
    Prentice-Hall, Inc., 1997. Chapter 7
  • MSY J. H. McClellan, R. W. Schafer, and M. A.
    Yoder, Signal Processing First, Prentice-Hall,
    Inc., 2003. Chapter 4
  • Haykin S. Haykin, Communication Systems, 4th
    ed., John Wiley Sons, New York, 2001. Chapter
    3
  • Lathi B. P. Lathi, Linear Systems and Signals,
    2nd ed., Oxford University Press, 2004. Chapter
    8
  • Sklar B. Sklar, Digital Communications, 2nd
    ed., Prentice-Hall, Inc., 2001. Chapter 2
  • ????????,?????,????,2007? ???
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