信号与系统

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1 (Signal & sysem) cqup.edu.cn

3 Z Z Z 3

5 . () Message Informaion Signal 5

6 . (2)

7 .. () (Deerminae signal) (Random signal) 7

8 .. (2) (Coninuous signal) (Discree signal) 8

9 .. (3) (Periodic signal) T f (+T )=f ( ) (Aperiodic signal) f (+T ) f ( ) 9

10 .. (4) (Energy signal) E P 0 (Power signal) P E (Non-power & non-energy signal) E P T 2 E = lim f ( ) d T T P T = 2 lim f ( d T 2T ) T 0

11 ..2 () U() Uni Uni sep signal U( ) = 0 < > 0 0 U() 0

12 ..2 (2) δ() Uni impulse signal : 0 0 δ ( ) = + δ ( ) d = = 0 () δ() 0 2

13 ..2 (3) δ() g () g ( ) = 0 < > 2 2 g () / / 2 0 / 2 3

14 ..2 (4) Complex exponenial signal e s s=σ +jω s s s=0 ω 0 e s e σ σ 0 e s e jω =cosω+ +jsinω 4

15 ..3 () f ()+f 2 (), f ()-f 2 (), f ()f 2 () f () 2 f 2 ()

16 ..3 (2) f () +f 2 () f () -f 2 ()

17 ..3 (3) 2 f () f 2 ()

18 ..3 (4) f() f(++ 0 ) f() 0 f() f(- 0 ) f() 0 f () f ( ) f (-)

19 ..3 (5) f() f(-) f() f () f (-)

20 ..3 (6) f() () df ( ) / d f ( ) 2 ( f ( ) d f ) ( ) () f () () () () (3) 3 2 f (-) ()

21 ..3 (7) f() f(a) ) : / /a a> ; a< ; f () f (2) f (0.5)

22 ..3 (8) f() f(-2-2) 2) f(-0.5 2) f(-2-2) 2) f() f (-2) f (2-2) 2) f (-2-2) 2) f() f (-2) f (--2) f (-2-2) 2) f() f (-) f (--2) f (-2-2) 2) f() f (-) f (-2) f (-2-2) 2) f() f (2) f (-2) f (-2-2) 2) f() f (2) f (2-2) 2) f (-2-2) 2) f ()

23 ..3 (9) f (-2) f (2-2) f (-2-2)

24 ..3 (0) f(-0.5+2) 0.5+2) f() f (+2) f (0.5+2) f (-0.5+2) f() f (+2) f (-+2) f (-0.5+2) f() f (-) f (-+2) f (-0.5+2) f() f (-) f (-0.5) f (-0.5+2) f() f (0.5) f (-0.5) f (-0.5+2) f() f (0.5) f (0.5+2) f (-0.5+2) 24

25 ..3 () f (+2) f (-+2) f (-0.5+2)

26 ..3 (2) f (-2) f () f (-2) f (-) f () - 0 f (+)

27 ..3 (3) f() f(-0.5 2) 2) f() f(-0.5+2) a =- = 6 b = 0 = 4 c,d = = 2 f (-0.5+2) c b d a f () b c a d

29 .2. Sysem Sysem 29

30 .2.2 () Coninuous sysem Discree sysem 30

31 .2.2 (2) Linear sysem Homogeneiy Homogeneiy x() y(); ax() ay() Superposiion propery x () y (), x 2 () y 2 (); x ()+ x 2 () y ()+ y 2 () x () y (), x 2 () y 2 (); ax ()+bx 2 () ay ()+by 2 () Nonlinear sysem 3

32 .2.2 (3) y()= )=x() 2 y()= )=x(- 0 ) y()= )= x() ) y()= )=q(0)+x () y()= )=q 2 (0)+x() y()= )=q(0)+x 2 () y()= )=q(0)x() 32

33 .2.2 (4) x()= )=U() q (0)= q 2 (0)=2 y ()=6e -2-5e -3 x()=3u() y 2 ()=8e -2-7e -3 x()=0 q (0)= q 2 (0)=2 y() 2 x()=2u() q (0)=q 2 (0)=0 y() : x()= )=U() q (0)=q 2 (0)=0 y zs (); x()=0 q (0)= q 2 (0)=2 y zi (); y zs () y zi () y ()= 6e6-2 -5e -3 3y zs () y zi () y 2 ()= 8e8-2 -7e -3 x()=0 q (0)= q 2 (0)=2 2 x()=2u() q (0)=q 2 (0)=0 y () y zi () 5e -2-4e -3 y () 2y zs () 2e -2-2e -3 33

34 .2.2 (5) Time invarian sysem x() y(); x(- 0 ) y( - 0 ) Time-varying sysem y()= )=x() 2 y()= )=x(- 0 ) y()= )=x() y()= )=x () y()= )=x(2) 34

35 .2.2 (6) Causal sysem Non-causal sysem y()=3x() y()= )=x(+) 35

36 .3 Model Model x() S y() x() S [q(0)] y() 36

38 .4. x () x 2 () y()= x ()+ x 2 () x () a y()= ax() x () y()= x()d 38

39 .4.2 () y +a 0 y=x y =x-a 0 y x () y() -a 0 39

40 .4.2 (2) y +a y +a 0 y=x y =x-a 0 y- a y x () y() -a -a 0 40

41 .4.2 (3) y +a y +a 0 y=b x +b 0 x q q + a q + + a 0 q=x y= b q +b 0 q b x () b 0 y() -a -a 0 4

42 .5 () 42

43 .5 (2) 43

44 .5 (3) δ ( τ ) U( τ ) j e ω e s δ ( k n) z k 44

信号与系统 (Signal & system)

信号与系统 (Signal & system) Signl & sysem xucb@cqup cqup.edu.cn 5-3- ...3.4.5 .......3 3 .. δ δ d δ 4 .. i K V CF u c i δ u c - 5 .. ϕ δ ϕ δ ϕ δ d ϕ ϕ δ ϕ δ ϕ δ d ϕ 6 .. e δ e δ δ δ δ 3δ δ π sin δ d 3 e δ d 3 δ d 5 4 7 .. 3 ϕ δ ϕ