第3章(5)

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Unformatted text preview: * 1¸ % 3 XX ª ¼ ªs z * H 3 − 16H x(t ) = e − 2t u (t )H y (t ) = ( ) 1 − t − 3t e − e u (t )H 2 H h(t ) H H ( jω ) H X ( jω ) = 1 jω + 2 1 1 1 1 Y ( jω ) = jω + 1 − jω + 3 = ( jω + 1)( jω + 3) 2 Y ( jω ) jω + 2 A B H ( jω ) = = = + X ( jω ) ( jω + 1)( jω + 3) j ω + 1 jω + 3 shi9876@hzcnc.com 1 * 1¸ % 3 XX ª ¼ ªs z * jω + 2 A= jω + 3 jω = −1 jω + 2 B= jω + 1 1 = 2 1 1 1 H ( jω ) = j ω + 1 + jω + 3 2 1 = 2 jω = −3 ( ) 1 −t h(t ) = e + e −3t u (t ) 2 3.6.3 LTI ¼ „ I H d 2 y (t ) dy (t ) dx(t ) H 3 − 17H +3 + 2 y (t ) = 2 + x(t )H 2 dt dt dt H h(t ) H H ( jω ) shi9876@hzcnc.com 2 * 1¸ % 3 XX ª ¼ ªs z * ( jω ) 2 Y ( jω ) + 3 jωY ( jω ) + 2Y ( jω ) = 2 jωX ( jω ) + X ( jω ) Y ( jω ) 2 jω + 1 H ( jω ) = = X ( jω ) ( jω ) 2 + 3 j ω + 2 2 jω + 1 −1 3 = = + ( jω + 1)( jω + 2) j ω + 1 jω + 2 ( ) h(t ) = 3e −2t − e − t u (t ) H 3 − 18H y '' (t ) + 4 y ' (t ) + 3 y (t ) = x ' (t ) + 2 x(t )H x(t ) = e − t u (t ) ª¼` V Þ 0H y (t ) shi9876@hzcnc.com 3 * 1¸ % 3 XX ª ¼ ªs z * H jω + 2 H ( jω ) = 2 ( jω ) + 4 jω + 3 Y ( jω ) = ( 1 X ( jω ) = jω + 1 jω + 2 A A12 A2 = 11 + + 2 jω + 1 ( jω + 1) 2 jω + 3 jω + 1) ( jω + 3) jω + 2 A2 = ( jω + 1) 2 1 =− 4 jω = −3 jω + 2 A12 = jω + 3 jω + 2 1 1 ( jω + 1) = A11 ( jω + 1) + − jω + 3 2 4 jω + 3 shi9876@hzcnc.com = jω = −1 1 2 2 4 * 1¸ % 3 XX ª ¼ ªs z * jω = 0 Y ( jω ) = 112 A11 + − = 2 12 3 1 A11 = 4 14 12 14 + − jω + 1 ( jω + 1) 2 jω + 3 1 −t 1 −t 1 − 3t y (t ) = e u (t ) + te u (t ) − e u (t ) 4 2 4 3.6.4 ¼ „ M 0 LTI § @ * ª¼ ˜ e6 H ( jω ) h* (t¼ ) ˜ ª e6 x(t ) = x(t + T ) shi9876@hzcnc.com y (t ) 5 * 1¸ % 3 XX ª ¼ ªs z * 1 x(t ) = ∞ ∑ ak e jkω 0 t k =− ∞ 2π ω0 = T e s0ª t 6 ¼ Þ` ª 26 ¼ Þ` 1 ak = T ∫ T x(t )e − jkω 0t dt H ( s0 ) e s 0 t e jkωª 0tÞ` ¼ H ( jkω 0 )e jkω 0t ∞ H ( jkω 0 ) = ∫ h(t )e − jkω 0t dt = H ( jω ) ω = kω 0 −∞ 3 x(t ) = ∞ ∑ ak e k =− ∞ jkω 0 t → y (t ) = ∞ ak H ( jkω 0 )e jkω 0t ∑ k =− ∞ shi9876@hzcnc.com 6 * 1¸ % 3 XX ª ¼ ªs z * H y ' (t ) + y (t ) = x(t )H x(t ) = cos(t )H h(t )H H ( jω ) H y (t ) j ωY ( jω ) + Y ( jω ) = X ( jω ) 1 H ( jω ) = jω + 1 h(t ) = e − t u (t ) ( 1 jt x(t ) = cos(t ) = e + e − jt 2 e jt → H ( j1)e jt = 1 jt e 1+ j ) e − jt → H (− j1)e − jt = shi9876@hzcnc.com 1 − jt e 1− j 7 * 1¸ % 3 XX ª ¼ ªs z * [ 1 1 e jt e − jt = e j (t −π x(t ) → y (t ) = + 2 1+ j 1− j 2 2 4) + e − j ( t −π 4) 1 π = cos t − 2 4 3.6.5 * ª1 ÈÞ ¼` 8 R s L s * C ÈÞ ª¼ ` vR (t ) = RiR (t ) dvC (t ) iC (t ) = C dt shi9876@hzcnc.com diL (t ) vL (t ) = L dt 8 * 1¸ % 3 XX ª ¼ ªs z * * 2 hÛ ª¼` R s L s * C hÛ ª¼` VR ( jω ) = RI R ( jω ) VR ( jω ) =R I R ( jω ) I C ( jω ) = jω C VC ( jω ) VC ( jω ) 1 = I C ( jω ) jω C VL ( jω ) = jωLI L ( jω ) VL ( jω ) = jωL I L ( jω ) H 3 − 19 p s v* (ª t¼ `) hÛ shi9876@hzcnc.com vC (t ) 9 * 1¸ % 3 XX ª ¼ ªs z * VC ( jω ) 1 jω C 1 1 H ( jω ) = = = = V ( jω ) R + 1 jω C 1 + jωRC 1 + 0.5 jω = 1 − 1 + π δ (ω ) 2 1 VC ( jω ) = jω + π δ (ω ) jω jω + 2 jω + 2 vC (t ) = u (t ) − e −2t u (t ) shi9876@hzcnc.com 10 * 1¸ % 3 XX ª ¼ ªs z * 3.6.6ª ¼ È * e4 y (t ) = K x(t − t0 ) 1 Àø * ª ¼ 2∪ e 4 * ª ¼ 3∪ 4e (1)∪ ª ¼ 4e (2)∪ ª¼ e 4 (3) h(t ) = Kδ (t − t0 ) H ( jω ) = Ke − jω t0 H ( jω ) = K K >0 φ (ω ) = −ωª ¼t0 ∪ * e4 dφ (ω ) τ (ω ) = − = t0 dω shi9876@hzcnc.com 11 * 1¸ % 3 XX ª ¼ ªs z * 3.6.7ª ¼ X * e0 1s ¼ „ N p e − jω t0 H ( jω ) = 0 ω < ωc other shi9876@hzcnc.com 12 * 1¸ % 3 XX ª ¼ ªs z * E ” y 2* sª hÌ Ð… ¼ s H 1 ( jω ) = H ( jω ) s H ( jω ) = H 1 ( j ω ) e − jω t 0 h1 (t ) = sin(ω c t ) πt sin ω c ( t − t0 ) h(t ) = h1 (t − t0 ) = π ( t − t0 ) E ” y Ð * 3 ¼ s„ L r ª t −t 0 sin ω τ sin ω c (τ − t0 ) c1 dτ = ∫ dτ 1 s (t ) = ∫ h(τ )dτ = ∫ −∞ −∞ −∞ π (τ − t0 ) πτ1 t t 1 = π ∫ ω c ( t −t 0 ) −∞ sin τ dτ τ shi9876@hzcnc.com 13 * 1¸ % 3 XX ª ¼ ªs z * sin(t ) Sa (t ) = t 1 s (t ) = π ∫ −∞ ω c ( t −t 0 ) −∞ 11 =+ 2π ª¼ e7 ∫ ∫ ∞ Sa (t )dt = π ω c ( t − t0 ) sin τ 1 0 sin τ sin τ dτ + ∫ dτ dτ = ∫ 0 π −∞ τ τ τ ω c ( t −t0 ) 0 π ∫−∞ Sa(t )dt = 2 0 sin τ dτ τ sin(τ ) Si (t ) = ∫ dτ 0 τ t 11 s (t ) = + Si[ω c (t − t0 )] 2π shi9876@hzcnc.com 14 * 1¸ % 3 XX ª ¼ ªs z * shi9876@hzcnc.com 15 * 1¸ % 3 XX ª ¼ ªs z * lim s (t ) = u (t − t0 ) ω c →∞ t = ª t 0e 2 *¼ ¸ % z X * 4¼ s• X ªq y (t ) ≈ x(t − t0 ) shi9876@hzcnc.com 16 * 1¸ % 3 XX ª ¼ ªs z * x(t − t0 ) j ` y (t ) (1) ω c y (t ) ( 2) τ y (t ) x(t − t0 ) x(t − t* 0 )2 ª( ¼ e τ >> 2π ωc x(t ) = cos(π t ) + 2 cos(3π t ) y (t ) ( ) 1 jπt x(t ) = e + e − jπt + e j 3πt + e − j 3πt 2 shi9876@hzcnc.com 17 * 1¸ % 3 XX ª ¼ ªs z * e jπt → H ( jπ )e jπt = e jπts e − jπt → H (− jπ )e − jπt = e − jπt e j 3πt → H ( j 3π )e j 3πt = 0 e − j 3πt → H (− j 3π )e − j 3πt = 0 ( ) 1 jπt y (t ) = e + e − jπt = cos(π t ) 2 shi9876@hzcnc.com 18 * 1¸ % 3 XX ª ¼ ªs z * *ªH ¼3 e P125 s 3.11 s 3.13 P126 s 3.16 s 3.17 s 3.19 s 3.21 s 3.21(1)(2) P127 s 3.24(2) ②④⑤ P127 s 3.27(1)(3) P128 s 3.29 s 3.31(1) P129 s 3.34 shi9876@hzcnc.com 19 ...
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This note was uploaded on 08/22/2011 for the course EE 201 taught by Professor Yhm during the Spring '05 term at Zhejiang University.

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