734604588_7_Ch1-作业解答-2010

f t f t 2 a 8 f t e t 2 u t 2 u

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Unformatted text preview: f (t )δ (t − t0 )dt = ∫ f (t0 )δ (t − t0 )dt = f (t0 ) ∫ ∫ ∞ −∞ ∞ (e −t + t )δ (t + 2)dt = e − ( −2) − 2 = e 2 − 2 e − jωt [δ (t ) − δ (t − t0 )]dt = e − jω 0 − e − jωt0 = 1 − e − jωt0 −∞ 1-18ªë “ ¹ * ( 1-18Ê ªº ¸ F ´ ™ Ð * * â p µ á f (t ) = f e (t ) + f o (t ) … (1) f e (t )“ (ë ª ¹ f e (t ) = f e (−t ) … f o (t ) = − f o ( −t ) … 1 ~ ë* 38 ¹ª ’ 2 3 f o (t ) ° º Ê 1 f e (t ) = [ f (t ) + f (−t )] 2 1 f o (t ) = [ f (t ) − f (−t )] 2 a *ª 8 ¹ f (t ) = e − (t − 2) [u (t − 2) − u (t − 3)] f ( −t ) = et + 2 [u (−t − 2) − u (−t − 3)] a-2 a-1 1 f e (t ) = [ f (t ) + f (−t )] 2 1 − ( t − 2) e ,2 ≤ t ≤ 3 2 ={ 1 t +2 e , −3 ≤ t ≤ −2 2 1 f o (t ) = [ f (t ) − f (−t )] 2 1 − ( t − 2) e ,2 ≤ t ≤ 3 2 ={ 1 − e t + 2 , −3 ≤ t ≤ −2 2 a-3 a-4 1 1-8(a) b * ïˆ ª ¹ 1 1 f (t ) = u (t + ) − u (t − ) 2 2 f e (t ) = f (t ) f o (t ) = 0 2 f (t ) = f (−t ) fe(t) 1 0.8 0.6 0.4 0.2 0 -0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 e2 1-18 b 1-20 á * â p µ 1) ) ) Linearityp™´F D ¾ mÐ ” ª x1 (t ) t x2 (t )•¹ øë D ª y1 (t ) t y2 (t ) t T [ x1 (t )] = y1 (t ) T [c1 x1 (t ) + c2 x2 (t )] = c1 y1 (t ) + c2 y2 (t ) “ — —@ F ´ › T [ x2 (t )] = y2 (t ) @›´FE T c7 @ ≅@jƒnRsâ F ´ › @ ø∠ F ´ š t 2) ª h¹ t t0 ¨ Causalityh D¹ ë • ª 3) ) D¹ ª •ë Dªª º ½ ˆ c D0 =¯ 2 c ¨ D¹ ø ª 1 •ë * D½ª º =c ª 02 c ¯ˆ 2¨ c1 t c2 t ”› F ´ Time-Invariabilityè F D¾ Ð m g ´ª™ t0 ¨ r (t ) = f [e(t )] D ¹t0ë ø• ª r (t − t0 ) = f [e(t − t0 )] t = t0 t < ª t0 D ¹ •ë y (t ) = T [ x(t )]ë η ª ¹ •D = h(t )u (t ) h (t ) = { ≠ h(t )u (t ) ¨ ¨ y (t1 ) = T [ x (t2 )], t1 < t2 3 = h ( n )u ( n ) h( n) = { ≠ h ( n )u ( n ) 7 r (t ) = ∫ e(τ )dτ −∞ t r...
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