734604588_7_Ch1-&auml;&frac12;œ&auml;&cedil;š&egrave;&sect;&pound;&ccedil;&shy;”-2010

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &lt; 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 &lt; t2 3 = h ( n )u ( n ) h( n) = { ≠ h ( n )u ( n ) 7 r (t ) = ∫ e(τ )dτ −∞ t r...
View Full Document

Ask a homework question - tutors are online