第1章(4)

第1章(4) - s>

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online