4.2> 2a (0)<2>X(j) 0+a P208 X(o)=0 0+a 幅频特性相同 相频特性不同 →时域信号不同 x(t) 2/a 图47)例42中考的并示于图4.6中 图4.6例4.2中的信号x(x)=e-a() 的信号的傅里叶变换 ProfJianyu Yang:Understanding of Signals Systems
<4.2> 2 2 2 ( ) ( ) ( ) a t a x t e u t X j a − = ⎯→ = + (a>0) (P208 2 2 1 X j ( ) ; a = + X j ( ) 0 = 幅频特性相同 相频特性不同 时域信号不同 2 F
4.3 F (1)=6(1)<>X(j)=1 X(o) 0 <Proof> ·0 ②X(j0)=x()eam 6(t)e Jot ProfJianyu Yang:Understanding of Signals Systems
x t( ) X j ( ) t 1 1 0 0 F <4.3 > x t t X j ( ) ( ) ( ) 1 = ⎯→ = F 2 <Proof> ( ) ( ) j t X j x t e dt + − − = 2 ( ) j t t e dt + − − = j 0 e − = = 1
4.4 TkT F x() →X(10)=2SnO 0,|t}>T x(t) 2T, X(o) F @=2T f O T (-kx)(%r <证明 ②X(j) x(te y dt e ot Jat O e J jOT e Jor mInoT 2J ProfJianyu Yang:Understanding of Signals Systems
<4.4> 1 1 1 1, | | sin ( ) ( ) 2 0, | | t T T x t X j t T ⎯→ = 2 F x t( ) X j ( ) 1 1 2T 1 T1 −T t = 2 f T1 − T1 F 1 ( ) 1 2T − 1 ( ) 1 2T ( ) f <证明> ( ) ( ) j t X j x t e dt + − − = 2 1 1 2 1 | 2 T T j t e j − − = 1 1 T T j t e dt − − = 1 1 1 T T j t de j − − = − 1 1 2 1 ( ) 2 j T j T e e j − = − 1 2sinT =
4.4 2T1 图48(0)例4中的矩形脉神信号 (b)它的傅里叶变换 少》 Prof Jianyu Yang: Understanding of Signals a systems
<4.4>
4.5> sin ,OkB x() BtAF→X(jo) 丌t B x() xo 丌 2r f B B B B 2B 2B <证明〉 +B B ④x() X(oe leor do= ot d de 2丌 2丌 2 jt J-8 Jot IB B e iBle iBt\三 sin bt 丌t2 nt 2 ProfJianyu Yang:Understanding of Signals Systems
<4.5 > sin 1, | | ( ) ( ) 0, | | Bt B x t X j t B = ⎯→ x t( ) X j ( ) 1 B t −B B B− B ( ) f 1 1 ( ) 2B − 1 ( ) 2B F F = 2 f <证明 > 1 1 ( ) ( ) 2 j t x t X j e d + − = 1 1 | 2 B B j t e t j = − 12 BB j t e d +− = 1 1 2 BB j t de jt +− = 1 1 ( ) 2 jBt jBt e e t j − = − sin Bt t =