第1章(4)

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Unformatted text preview: s> 7¬1 Õ ˆ* ª ½ Î 1.6 ¶ h * ª æ. 1.6.1 x1 (t ) → y1 (t ) x2 (t ) → y2 (t ) x3 (t ) = x1 (t ) + x2 (t ) → y3 (t ) y3 (t ) = y1 (t ) + y2 (t ) a x4 (t ) = ax1 (t ) → y4 (t ) y4 (t ) = ay1 (t ) a 5– . • á + ªh ¶ æ . [email protected] 1 s> 7¬1 Õ x ª ½ Î* x(t ) = 0y e¸ y (t ) = 0 1.6.2 ð < ª¶ x1 (t ) → y1 (t ) x2 (t ) = x1 (t − t0 ) → y2 (t ) y2 (t ) = y1 (t − t0 ) 5– . • á + * <¶ ªð s y e¸ LTI s y[n] = 2 x[n] + 3 e ¸ ð* T ª <¶ x1[n] → y1[n] = 2 x1[n] + 3y x2 [n] → y2 [n] = 2 x2 [n] + 3 x3 [n] = x1[n] + x2 [n] → y3 [n] = 2( x1[n] + x2 [n]) + 3 ≠ y1[n] + y2 [n] [email protected] 2 s> 7¬1 Õ ¸* ª ½ Î @* ° n E Œ Ð ª %½ (¸¶ *. ª æ x[n] = 0 ) y[n] = 3 ≠ 0 % ø y x1[n] → y1[n] = 2 x1[n] + 3 x2 [n] = x1[n − n0 ] → y2 [n] = 2 x1[n − n0 ] + 3 y1[n − n0 ] = 2 x1[n − n0 ] + 3 y2 [n] = y1[n − n0 ] % ø y t y (t ) = ∫ x(τ )dτ % ø * ÷¶ ª æ . −∞ [email protected] 3 s> 7¬1 Õ x ª ½ Î* t t −∞ −∞ x1 (t ) → y1 (t ) = ∫ x1 (τ )dτ x2 (t ) → y2 (t ) = ∫ x2 (τ )dτ x3 (t ) = a1 x1 (t ) + a2 x2 (t ) → y3 (t ) = ∫ t −∞ t t −∞ [ a1 x1 (τ ) + a2 x2 (τ )] dτ −∞ y3 (t ) = a1 ∫ x1 (τ )dτ + a2 ∫ x2 (τ )dτ = a1 y1 (t ) + a2 y2 (t ) *ªΗ ¶ð 3 t x1 (t ) → y1 (t ) = ∫ x1 (τ )dτ x2 (t ) = x1 (t − t0 ) −∞ t t −∞ −∞ y2 (t ) = ∫ x2 (τ )dτ = ∫ x1 (τ − t0 )dτ = ∫ y1 (t − t0 ) = ∫ t −t0 −∞ t −t 0 −∞ x1 (λ )dλ x1 (τ )dτ = y2 (t ) . ¸ [email protected] 4 s> 7¬1 Õ À ª ½ Î* y (t ) = x(2t ) 1 m *ª8 ¶ æ . y1 (t ) = x1 (2t ) y2 (t ) = x2 (2t ) x3 (t ) = a1 x1 (t ) + a2 x2 (t ) → y3 (t ) = x3 (2t ) = a1 x1 (2t ) + a2 x2 (2t ) y3 (t ) = a1 y1 (t ) + a2 y2 (t ) 1 x1 (t ) → y1 (t ) = x1 (2t ) x2 (t ) = x1 (t − t0 ) x2 (t ) → y2 (t ) = x2 (2t ) = x1 (2t − t0 ) y1 (t − t0 ) = x1 (2(t − t0 )) = x1 (2t − 2t0 ) ≠ y2 (t ) *ª8 ¶ .æ [email protected] 5 s> 7¬1 Õ À ª ½ Î* 1.6.3¿ ð ªi ŒE*Ð@ ª ¶ ˆæe * y (t ) = 2 x(t ) + 3¶ ˆæe ª* [email protected] 6 s> 7¬1 Õ * ª ¿ Î 5– . • á + *æ ª' (¶ (æ * (¶ 'ª )æ 'ª (¶ ∆y (t ) = y2 (t ) − y1 (t ) ∆x(t ) = x2 (t ) − x1 (t ) ∆y (t ) = 2∆x(t ) *æ 'ª (¶ ∆x(t ) + H ∆y (t ) æ 'ª (¶ +H y x(t ) = 0y y (t ) = 3 ~'ª ¶ (æ * y zi (t ) = 3 = [email protected] 7 s> 7¬1 Õ ¸* ª ½ Î 1.6.4 W` 5– . • á + ªH æ &¶ y (t ) = 2 x(t ) + 3 y (t ) = x 2 (t ) y t y (t ) = ∫ x(τ )dτy y[n] = x[n] − x[n − 1]y y (t ) = x(t ) sin(t − 1) −∞ ª¶ æΗ & 1.6.5 W` 5– . • á + ªH æ &¶ [email protected] 8 s> 7¬1 Õ * ª ¿ Î y (t ) = 2 x(t − 1) y[n] = n ∑ x[k ] k =− ∞ * ª ø∋ ¶ æ ª ø∋ ¶ æ @* ª €Σ E ŒÐ k ½ y ª ø∋ ¶ æ 1 { x[n − 1] + x[n] + x[n + 1]} ª ¶ æ ø' 3 ª ¶ æ ø' y (t ) = x(−t ) y (t ) = x(t − 1) cos(t + 1) y y[n] = 1.6.6 * ª¶ æ ' *0 x1 (t ) ≠ x2 (t ) y1 (t ) ≠ y2 (t ) [email protected] 9 s> 7¬1 Õ * ª ½ Î x(t ) y (t ) = 2 y (t ) = 2 x* (tª )(æ ¶ # * ª (æ ¶ # y (t ) = sin x(t ) x2 (t ) x1 (t ) + 2π x2 (t ) ≠ x1 (t ) y2 (t ) = y1 (t ) y (t ) = sin x(ª t ¶ )(æa * [email protected] 10 s> 7¬1 Õ ˜* ª ½ Î * )¶ æ ª y (t ) = x(t − t0 ) y (t ) = x(t + t0 ) dx(t ) y (t ) = dt t y (t ) = ∫ x(τ )dτ −∞ y[n] = n ∑ x[k ] y[n] = x[n] − x[n − 1] y k =− ∞ 1.6.7 ª¶ æ) [p VH BIBO [p ª¶ æ) x(t ) < M in [email protected] y (t ) < M out 11 s> 7¬1 Õ * ª ½ Î 5– . • á + ªÈæ $¶ s y (t ) = x (t )s y (t ) = e s y (t ) = tx(t )s y[n] = 2 x (t ) n ∑ x[k ] k =− ∞ s y (t ) = x 2 (t )s x(t ) < Ms y (t ) < M 2È$æ ª¶ y (t ) = e x ( t ) x(t ) < M y (t ) < e M ∪¶ ª $æ s x(t ) = u (t )s x(t ) ≤ 1s y (t ) = tu (t* )È$æ ª¶ [email protected] 12 s> 7¬1 Õ ¸* ª ½ Î * ª -¨ æ ¶ P26 s 1.4(a)(e) P28 s 1.18 P26 s 1.5(2)(3) P28 s 1.19 P26 s 1.6 P26 s 1.7(2)(3)(4) P26 s 1.9 P27 s 1.11(1)(2)(5)(6) P27 s 1.14 [email protected] 13 ...
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