第3章(4)

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Unformatted text preview: * 1 · º 3 è ¸* ª · ªs h 3.5.9ª · ¸ * ‘… FT x(t ) ←→ X ( jω )j (1)j x(tª … )¸‘ *· ∫ j ∞ −∞ 1 x(t ) dt = 2π 2 Ip ∫ ∞ −∞ 2 X ( jω ) dω =s (2)s x(t ) = x(t + T )s ∞ ak e jkω 0ts ∑ x(t ) = k =− ∞ s 9 Ð * ª Š E Æ L · 1 T ∫ 2 T x(t ) dt = ∞ ∑ ak 2 k =− ∞ = p shi9876@hzcnc.com 1 * 1 · º 3 è ¸* ª · ªs h 3.5.10ª · ˆ * ‘‡ FT (1) x(t ) * h(t ) ←→ X ( jω ) H ( jω ) 1 x(t ) = 2π ∫ ∞ −∞ X ( jω )e jω t dω e jω t → H ( j ω ) e j ω t 1 x(t ) → y (t ) = 2π ∫ ∞ −∞ X ( j ω ) H ( j ω ) e jω t d ω FT y (t ) ←→ Y ( jω ) = X ( jω ) H ( jω ) shi9876@hzcnc.com 2 * 1 · º 3 è ¸* ª · ªs h j x(t ) * h(t ) j x(t ) = 1 + u (t + 1) 1 jω X ( jω ) = 2π δ (ω ) + + π δ (ω ) e jω e jω e jω = 2π δ (ω ) + + π δ (ω ) = + 3π δ (ω ) jω jω shi9876@hzcnc.com 3 * 1 · º 3 è ¸* ª · ªs h e − jω H ( jω ) = 1 + jω h(t ) = e − ( t −1)u (t − 1) e jω e − jω x(t ) * h(t ) ←→ X ( jω ) H ( jω ) = + 3π δ (ω ) jω 1 + jω FT 1 1 1 = + 3π δ (ω ) = − + 3π δ (ω ) jω (1 + jω ) jω j ω + 1 = 1 1 + π δ (ω ) − + 2π δ (ω ) jω jω + 1 x(t ) * h(t ) = u (t ) − e − t u (t ) + 1 shi9876@hzcnc.com 4 * 1 · º 3 è ¸* ª · ªs h sin(50π t ) x(t ) = πt sin( 20π t ) h(t ) = πt y (t ) = x(t ) * h(t ) 1 ω < 50π sin(50π t ) FT x(t ) = ←→ X ( jω ) = πt 0 ω > 50π 1 ω < 20π sin( 20π t ) FT h(t ) = ←→ H ( jω ) = πt 0 ω > 20π 1 ω < 20π Y ( jω ) = X ( jω ) H ( j ω ) = 0 ω > 20π y (t ) = x(t ) * h(t ) = h(t ) shi9876@hzcnc.com 5 * 1 · º 3 è ¸* ª · ªs h (2) x1 (t ) x2 (t ) = ) T x1 (t ) ⊗ x2 (t ) = ∫ x1 (τ ) x2 (t − τ )dτ ← FS→ Ta1k a2 k T ª Š‘ · x1 (t ) ⊗ x2 (t ) = ∫ x1 (τ ) x2 (t − τ )dτ T x1 (t ) = x2 (* t ª) Š‘ · x1 (t ) ⊗ x2 (t ) shi9876@hzcnc.com 6 * 1 · º 3 è ¸* ª · ªs h 2 y (t ) = x1 (t ) ⊗ x2 (t ) = ∫ x1 (τ ) x2 (t − τ )dτ −2 shi9876@hzcnc.com 7 * 1 · º 3 è ¸* ª · ªs h 3.5.11 · F¸ Œ 1 Y ( jω ) = X 1 ( jω ) ∗ X 2 ( jω ) 2π y (t ) = x1 (t ) x2 (t ) j j ∞ X 1 ( jω ) ∗ X 2 ( jω ) = ∫ X 1 ( jλ ) X 2 ( j (ω − λ ))dλ −∞ X ( jω )j x(t )j x(t )cos(ω 0t )j FT x(t ) ←→ X ( jω ) FT cos(ω 0t ) ←→ π [δ (ω − ω 0 ) + δ (ω + ω 0 )] 1 x(t ) cos(ω 0t ) ←→ [ X ( j (ω − ω 0 ) ) + X ( j (ω + ω 0 ) ) ] 2 FT shi9876@hzcnc.com 8 * 1 · º 3 è ¸* ª · ªs h ª† ·‘ ˆ j sin(10π t ) sin(20π t ) x(t ) = ⋅ πt πt 1 ω < 10π sin(10π t ) FT x1 (t ) = ←→ X 1 ( jω ) = πt 0 ω > 10π 1 ω < 20π sin( 20π t ) FT x2 (t ) = ←→ X 2 ( jω ) = πt 0 ω > 20π shi9876@hzcnc.com 9 * 1 · º 3 è ¸* ª · ªs h x(t ) ∞ y (t ) = x(t ) ∑ δ (t − kT ) k =− ∞ T = 0.1 δ T (t ) ←→ ω 0 FT Y ( jω ) 0 .2 ∞ ∑ δ (ω − kω k =− ∞ 0 ) shi9876@hzcnc.com 2π ω0 = T 10 * 1 · º 3 è ¸* ª · ªs h (1)T = 0.1 ω 0 = 20π (2)T = 0.2 ω 0 = 10π shi9876@hzcnc.com 11 * 1 · º 3 è ¸* ª · ªs h 3.6 LTI ·s‘ • ( ª 3.6.1 * ªL‘ TI ( ·• ∞ h(t ) ←→ H ( jω ) = ∫ h(t )e − jω t dt FT * ª · ‘ • 1( −∞ 2 y zs (t ) = x(t ) * h(t ) Yzs ( jω ) = X ( jω ) H ( jω ) H ( jω ) = Yzs ( jω ) X ( jω ) 3 − 12 ⸠y (t ) = dx(t ) dt Y ( jω ) = jωX ( jω ) shi9876@hzcnc.com H ( jω ) = jω 12 * 1 · º 3 è ¸* ª · ªs h 3 − 13 ) H )H j u (t ) 1 H ( jω ) = + π δ (ω ) jω j 3 − 14 ) H j y (t ) = x(t − t0 ) Y ( j ω ) = e − jω t 0 X ( j ω ) H ( j ω ) = e − jω t 0 ª · ‘ hŒ H ( jω ) = 1 ª · ‘ η Œ shi9876@hzcnc.com Arg[ H ( jω )] = −ω t0 13 * 1 · º 3 è ¸* ª · ªs h 3.6.2 E Æ 9 Ð *Lª TI ˜ · •0 j 3 − 15j h(t ) = e − at u (t )j x(t ) = e − bt u (t )j a > 0j b > 0j s y zs (t ) 1 1 H ( jω ) = s X ( jω ) = jω + a jω + b Y ( jω ) = X ( jω ) H ( j ω ) = s a ≠ bs 1 ( j ω + a ) ( jω + b ) 1 1 1 Y ( jω ) = jω + a − jω + b b−a shi9876@hzcnc.com 14 * 1 · º 3 è ¸* ª · ªs h ( ) 1 y (t ) = e − at − e −bt u (t ) b−a 1 a=b Y ( jω ) = ( jω + a ) 2 *ªΗ · ‡‘ y (t ) = te − at u (t ) 1 A B f ( x) = = + ( x + a )( x + b) x + a x + b As 1 x+a = A+ B x+b x+b Bs 1 x+b = A+ B x+a x+a shi9876@hzcnc.com 1 b−a s x = − as A= s x = −bs 1 B= a −b 15 * 1 · º 3 è ¸* ª · ªs h 2 · 2ð Œ 1 A1 A2 B f ( x) = = + + 2 2 ( x + a ) ( x + b) x + a ( x + a ) x+b A1s 1 ( x + a) 2 = A1 ( x + a) + A2 + B x+b x+b x 1 2( x + a )( x + b) − ( x + a ) 2 − = A1 + B 2 2 ( x + b) ( x + b) x = −a 1 A1 = − (b − a) 2 shi9876@hzcnc.com 16 ...
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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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