2014春信号09第八讲3912done

1、 7?u?f?X2014 cSG?&?X?1l?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C?

2、? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(?&? Fp?C?2014 S&?X?1l?Fp?Fp?C?Fp? 7Fp?C?ZZt0+T1Jj1T1jn1tdtFn =f (t)eF () =f (t)ejtdt3.9 ?&? Fp?C?t0ZXsin?cos?&?1ejn1tF ()ejtdf (t) =Ff (t) =n23.10 ? &? Fp?C? ? n=I?&? ?u?&?C?&?l?L?Y?Fp?C?Fp?C?&?E ?,?v? 3?-? ?:

3、?&? Fp?C?E,3?Fp?Fp?C?n?&?&?5?5?L?(?3.11 ? ?n? ?n? ?nI3.12 X? n!X?&? ?I? (? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos3.10 ? &? Fp?C? ? ?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(?sin?cos Fp?C?2014 S&?X?1l?F 1 = 2()?d?

4、A5? F ej1t = 2( )F ej1t = 2( + ) 711Jj|?5?.? 3.9 ?&? Fp?C?sin?cosF cos(1t)?&? 13.10 ? &? Fp?C? ? j tj t= Fe+ e112= ( + 1) + ( 1)3.11 ? ?n? ?n? ?nF sin(1t)3.12 X? n!X?&? ? 1j tj t= Fe e11? (2j? ?(?= j ( + 1) ( 1)sin?cos Fp?C?2014 S&?X?1l?N? n 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n?

5、 ?n3.12 X? n!X?&? ? (? ?(?I?)? ? 2?&?!?&?X?&? Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos3.10 ? &? Fp?C? ? ?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(?&? Fp?C?2014 S&?X?1l?g? 7Jj3.9 ?&? Fp?C?sin?cos周期信号主值区间?&?3.10 ? &? Fp

6、?C? ? 叶变换叶级数叶变换3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(?&? Fp?C?2014 S&?X?1l?&? Fp?C? 7I?&?Fp?/?JjI?&?f (t) Fp?C?d? ?-?|?3.9 ?&? Fp?C?sin?cosXejn1tf (t) =Fn?&?n=3.10 ? &? Fp?C? ? ?I? ?-? m? ?u&? ?:0, 1, 21, z?- r? u &?Fp? ?AX?FnZt0+T1 1 f (t)ejn1tdtFn =T13.11 ? ?n? ?n? ?nt0I?Fp?C?I3.12 X? n!X?&? ?XF

7、f (t) = 2Fn( n1)? (n=? ?(?&? Fp?C?2014 S&?X?1l?&? Fp?m Fp?C? 7I?f0(t)?&?f (t) ?m?=Jj3.9 ?&? Fp?C?sin?cosf0(t) = f (t) u(t) u(t T1) f0(t) Fp?C?F0()?f (t) Fp?X?Fn?&?I3.10 ? &? Fp?C? ? ZZT1jtdt =jtdtF0() =f0(t)ef (t)e3.11 ? ?n? ?n? ?n0ZT1 11T1f (t)ejn1tdt = F =F ()n0 3.12 X? n!X?&? ?T10=n1I?&?f (t) Fp?

8、X?Fn? u?m &?f0(t) Fp?C?F0()3n1?: ? ? (? ?(?&? Fp?C?2014 S&?X?1l?&? Fp?C?m Fp?C? 7XF () = 2Fn( n1)Jjn=3.9 ?&? Fp?C?sin?cosX2=T1F ()|( n )01=n1?&?n=3.10 ? &? Fp?C? ? X= 1F0(n1)( n1)n=3.11 ? ?n? ?n? ?nI?&?f (t) Fp?C?d? m? ?u ?3.12 X? n!X?&? ?0, , 2 , ?-?|? u?11?&?f0(t) Fp?C?F0()3n1?: ? ?F () ?/GdF0()?-

9、m?d?T1?d?m ?F0()?T1? ?&?F ()? (II? ?(?&? Fp?C?2014 S&?X?1l?I?S T (t) Fp?C? 7XT (t) =(t nT1)Jjn=3.9 ?&? Fp?C?sin?cos?&?)3.10 ? &? Fp?C? ? IT (t) Fp? X?3.11 ? ?n? ?n? ?nZT1 2 1 T11 (t)ejn tdt =F =1nT3.12 X? n!X?&? ?T1T1 2I=? (X1? ?(?ejn1tT (t) =T1 n=?&? Fp?C?)?Y?2014 S&?X?1l?Il ? 7XXF T (t) = 2Fn( n1)

10、 = 1( n1)Jjn=n=3.9 ?&? Fp?C?sin?cos=?-G ?-G?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(?&? Fp?C?2014 S&?X?1l?I?/?&?f (t) ?E? ?T1?Fp?Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos)?&?I?/?&?f0(t) Fp?C?3.10 ? &? Fp?C? ? F () = E Sa023.11 ? ?n? ?n? ?nI? ?/?&? Fp?X? 1En1Fn =F ()=Sa3.12 X? n!X?&? ? 0TT211=

11、n1I=f (t) Fp? ( ? ?(?XET1n 12ejn1tf (t) =San=?&? Fp?C?2014 S&?X?1l?)?Y?I?dF0() ?f (t) Fp?C? 7 XJjn 12F () = E1Sa( n1)3.9 ?&? Fp?C?sin?cosn=?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(?&? Fp?C? Fp?C?2014 S&?X?1l?f1(t) E 7Jj0t02 T2 TT3.9 ?&? Fp?C?sin?cos22f3(t) E?&?3.10 ? &? Fp?C? ? t2

12、 T2 T0T0223.11 ? ?n? ?n? ?nf5(t) EF5()5E3.12 X? n!X?&? ?tT0T02 T2 22? (f7(t) EF7()7E? ?(?tT0T02222F3()3EF1()1E?&? Fp?C?2014 S&?X?1l?Cz5?T1k? 7F ()(E1)Jj3.9 ?&? Fp?C?sin?cos01 2?&?3.10 ? &? Fp?C? ? F ()(E1)3.11 ? ?n? ?n? ?n012 3.12 X? n!X?&? ?F ()? (E1)? ?(?012 f(t)E0T1t2f(t)E0T1t2f(t)E0 T1t2?&? Fp?C

13、?2014 S&?X?1l?Cz5?/G? k? 7FnJj3.9 ?&? Fp?C?sin?cos(E1)012 ?&?Fn3.10 ? &? Fp?C? ? (E1)3.11 ? ?n? ?n? ?n0123.12 X? n!X?&? ?Fn(E1)? (? ?(?021f(t)E0 T1t2f(t)E0 T1t2f(t)E0 T1t2?&? Fp?C?2014 S&?X?1l?|?nn)?&? Fp?C? 7f0(t) EJj3.9 ?&? Fp?C?sin?cos 0t02 2 2?&?3.10 ? &? Fp?C? ? FT (t)(1)3.11 ? ?n? ?n? ?n01tT10

14、T13.12 X? n!X?&? ?f(t)EF ()(E )1? ( ? ?(?0t0 2 2T1T12 2T1T (t)(1)?&? Fp?C?2014 S&?X?1l?(? 7Jj3.9 ?&? Fp?C?sin?cos非周期信号周期延拓周期信号( )*d tT?&?3.10 ? &? Fp?C? ? 叶变换叶相同变换3.11 ? ?n? ?n? ?n非周期信号的谱冲激函数抽样d (w - nw1 )周期信号的谱3.12 X? n!X?&? ? (? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?

15、sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(? &? Fp?C?2014 S&?X?1l? ? &? 7I|? ?S p(t)l?Y?m&?f (t)?/? 0?X l? ?l?&?/? &?0?fs(t)L?Jj3.9 ?&? Fp?C?sin?cos?&? L?% ?K3.10 ? &? Fp?C? &?fs(t) Fp?C? /G? ?Y&?f (t) Fp?C?k?X? &? 3 &?f (t) ?

16、k&E?3?o?e?l? &1.? ? 3.11 ? ?n? ?n? ?n2.3.12 X? n!X?&? ?3.? (?f (t)? ?E? ?s? ?(?Y&?f (t)? &? Fp?C?2014 S&?X?1l? A 7Jj连续信号f (t )数字信号f (n)抽样信号3.9 ?&? Fp?C?sin?cos?&?抽样量化编码(t )fs3.10 ? &? Fp?C?抽样脉冲 p (t )? ? 3.11 ? ?n? ?n? ?nI &? ?nC? &? ?2?z!?C?i&? D?n ?=?fX? ?|?d; ?y? ?z?d ?=? ? ?I3.12 X? n!X?&? ?I? (

17、? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(? 2014 S&?X?1l? ?S Fp?C?p(t)?&?k? &? Fp?C?fs(t) = f (t)p(t)?d?n?k1 7XJjP () = 2P ( n )ns3.9 ?&? Fp?C?sin?cos?&?F

18、s() = 2 F () P ()n=X?Pn =Z Ts=P F ( n )13.10 ? &? Fp?C?ns2jn tp(t)esdtn=TsTs? 2? 3.11 ? ?n? ?n? ?nX? &? ?Fs()?3.12 X? n!X?&? ?I?Y&? ?F ()? ?s ? p(t) Fp? X?Pn 5?Pn? ? ?E? /G?C?Cz? (I? ?(? 2014 S&?X?1l?/? ?g,? ? 7I?/?S Fp? X?Jj 3.9 ?&? Fp?C?sin?cos?&? 1En s2Pn =P ()=Sa 0TTss=ns3.10 ? &? Fp?C?I? X? F (

19、) =P F ( n )sns3.11 ? ?n? ?n? ?nn=I 3.12 X? n!X?&? ? XETsn s2F () =SaF ( n )ss? (n=? ?(? ?/? 2014 S&?X?1l? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(? 2014 S&?X?1l?-? ?n? ? 7I?-S Fp?Jj 3.9 ?&? Fp?C?sin?cos?&? 1Ts 1TsPn =P ()= 0=ns3.10 ? &? Fp?C?I? X? F () =P

20、F ( n )sns3.11 ? ?n? ?n? ?nn=I 3.12 X? n!X?&? ?X 1F () =F ( n )ssTs? (n=? ?(? ?-? 2014 S&?X?1l? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(? 2014 S&?X?1l?(? 7Jj3.9 ?&? Fp?C?sin?cos?&?冲激函数抽样连续信号离散信号( )d tT3.10 ? &? Fp?C?叶变换叶相同? ? 变换3.11 ? ?n? ?n? ?n连续信号的谱周期延拓*d

21、 (w - nw1 )离散信号的谱3.12 X? n!X?&? ? (? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(? 2014 S&?X?1l? &? Fp?C? 7I? =F1() = F ()P ()?d?n?kf1(t) = f (t) p(t)Jj3.9 ?&

22、? Fp?C?sin?cos?&?Ib P ()?m?1 ?-S ?P=P () =( n )?_C?1n=3.10 ? &? Fp?C? X 1 p(t) = 1 (t nT ) = (t)1T1 n=1? 3.11 ? ?n? ?n? ?nI?zk3.12 X? n!X?&? ?XX 1 ) =1 f (t) = f (t) (t nTf (t nT )1111 n=1 n=? (IeF () m?1 ?-S 3? ?K? ?f (t)?T1 ?=?&? ?l? ? ?(? ? &? Fp?C?2014 S&?X?1l? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &

23、? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(? &? Fp?C?2014 S&?X?1l? ? ?E ?AX 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(?I3-12g?&?T1l?1 = 2 T1? &?Ts = 2?E?ssJj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10

24、 ? &? Fp?C? ? 3.11 ? ?n3.11 ? ?n? ?n? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n3.11 ? ?n? ?n? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(? ?n2014 S&?X?1l? ?EX?抽样恢复 7f (

25、t )fs (t )f1 (t )H (w)Jj3.9 ?&? Fp?C?sin?cos?&?p (t )3.10 ? &? Fp?C? ? ?Y&?!? ?E?3.11 ? ?n? ?nf (t) = E 1 + cos(1t)? ?n3.12 X? n!X?&? ?Xp(t) = (t nTs)? (n=(2 ,? ?(?s| ;s0,2H() =elsewhere.? ?n? ? ?EL?2014 S&?X?1l? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(? ?n

26、k? ? ?EL?2014 S&?X?1l? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n? ?n3.12 X? n!X?&? ? (? ?(? ?n2014 S&?X?1l? 7I?&?f (t)?XJ?m, m?m?K&?f (t) ? m? ? ?/L? m?7LJj?u 1 ?m = 2fm?$? ?3.9 ?&? Fp?C?sin?cos?&?2fm?2fm3.10 ? &? Fp?C? ? IXJ? ? u2fm?y?U?K?U2?E?f (t)?N ?U? ?E?f (t)?&? ?/?U3?mS )?I3.1

27、1 ? ?n? ?n !? Cz? ?p? ?m? ?n3.12 X? n!X?&? ?I? 3,? &E?3T? ?m?S? ? ?g#N ?$? ?/G?dA?Nyquist?0? m?/G?dA? m?0? (I? ?(?Jj2014 S&?X?1l?3.9 ?&? Fp?C?sin?cos Fp?C?&? Fp?C? 7Jj3.9 ?&? Fp?C?sin?cos?&?3.10 ? &? Fp?C? ? 3.10 ? &? Fp?C? ? 3.11 ? ?n? ?n3.11 ? ?n? ?n? ?n? ?n3.12 X? n!X?&? ? (3.12 X? n!X?&? ? ?(? ?n2014 S&?X?1l? 7? ?nJjIe&?f (t)?m?&?8?3tm, tm ?m?3.9 ?&? Fp?C?sin?cos?&?S?e3?u 1 ?m?f (t) ?F () ?2tm1? ?K? ?F1()?/L? &?3.10 ? &? Fp?C? ? ?nVg3.11 ? ?n? ?nI3? uf (t)3?/?&?f1(t)? ?n? m?u 1 ?=? ?E? u2tm?K3.12 X? n!X?&? ?2