Linear Time-Invariant Systems

1
??? ???????

• Linear Time-Invariant Systems

????
2
Linear Time-Invariant Systems

• 2-0 ??
• 2-4 ?????????????LTI??
• 2-2 ????LTI??????
• 2-1 ????LTI?????
• 2-3 ??????????

3
?????
1.?????? 2.???????
4
?????
1.?????? 2.??????? ?????????????????????,??????
5
2-1 ????LTI?????
6
2-1 ????LTI?????
1.??? Convolution Sum

• ????x(n) ---????
• ????y(n) ????

(1)??????????????? (2)??????y(n)--??? (3)???????
7
1.???(Convolution Sum)
(1)???????????????
8
1.???(Convolution Sum)
??1??x(n)3,-1,-2,2,1,-2,2,-1,-3,
?????????
X(n)
x(-4)
x(0)


x(1)
9
1.???(Convolution Sum)
(2)??????y(n)--???
??1??x(n)3,-1,-2,2,1,-2,2,-1,-3,?????h(n)1,1
???
10
1.???(Convolution Sum)
(3)???????
11
2.?????(Convolution Sum)
???????
??2 ????x(n)???????h(n) ??,?????

• ?????n--k
• ?h(k)????h(-k)
• h(-k)??n???h(n-k)
• ??
• ??

????
12
2.?????(Convolution Sum)
??3 ????x(n)???????h(n) ??,?????
13
2.?????(Convolution Sum)
??3 ????x(n)???????h(n) ??,?????
14
2-3 LTI????Properties of LTI Systems
??

• ?????????????????
• ??LTI??????????????????
• ?????????????

???? ????
????????
??????????????????
15
2-3 LTI????Properties of LTI Systems

• ??/?????????
• ??????????????????

????h(t)/h(n)??????
16
2-3 LTI????Properties of LTI Systems

• 1. LTI??????Causality

• ???Causality?
• ?????????
• ?????0?,h(t)/h(n)?
• ????????
• ??

17
2-3 LTI????Properties of LTI Systems

• 2. LTI??????Stability

• ???Stability ?
• ?????????
• h(t)/h(n)?
• ????????
• ??

18
2-3 LTI????Properties of LTI Systems

• 3. ?????Commutative

• ???
• ????

19
2-3 LTI????Properties of LTI Systems

• 3. ?????Commutative

• ???
• ????
• ??
• ??????????????????,?????h(t)
• ???????????
• ????????????????

20
2-3 LTI????Properties of LTI Systems

• 4. ?????Distributive

• ???
• ????

21
2-3 LTI????Properties of LTI Systems

• 4. ?????Distributive

• ???
• ????
• ??

22
2-3 LTI????Properties of LTI Systems

• 5. ?????Associative

• ???
• ????

23
2-3 LTI????Properties of LTI Systems

• 5. ?????Associative

• ???
• ????
• ??
• ??????????????????h(n)???,
• ?????????

24
2-3 LTI????Properties of LTI Systems

• 6. ?????????

• g(t)?h(t)??
• ??????????

25
2-3 LTI????Properties of LTI Systems

• 6. ?????????

??????
26
2-3 LTI????Properties of LTI Systems

• 6. ?????????

??????
27
??

• ??
• P98-1(a) P98-3
• P99-14 P99-15

28
??

• ??1 ?????????

29
??

• ??2 ?????,??N???9,??
• ?N?