第1章(2)

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Unformatted text preview: s > 1¬ h ª » 7e ÎÕ 2e ª xz s» δ (t ) D Ü ‰ e ª (» 1)³ ` Ðk lim x∆ (t ) = δ (t ) ∆ →0 @ z»ªe ξ ①xΔ(t) s → @x»ªe 0 z xΔ(t@ )z x»ªe t = 0z » xª @ ②xΔ(t) s t = 0 s € → +∞ s ③7 » oªe D Ü ‰ Ð ∫ ∞ −∞ [email protected] x∆ (t )dt = 1 1 s > 1¬ h ª º 7e ÎÕ D Ü ‰ eª º S Ð (2)þ ` lim x∆ (t ) = δ (t ) ∆ →0 (3) ˆb7 » t≠0 ① ② ∫ ∞ −∞ δ (t ) = 0 δ (t )dt = 1 [email protected] 2 s > 1¬ Hª » 7e ÎÕ (4) δ(t)@ 6 ª {» lim x1∆ (t ) = δ (t ) ∆ →0 x2 ∆ (t ) = 2 x1∆ (t ) lim x2 ∆ (t ) = 2δ (t ) ∆ →0 (-∞ → + ∞)@ {»ªe °g (5) ° δ (t − t0 ) [email protected] 3 s > 1 ¬ àÕe ª º 7 Î δ (t − t0 ) = 0 t ≠ t0 δ (t − t0 ) ∞ ∫−∞ δ (t − t0 )dt = 1 (6)u(t) s δ(t) s t u (t ) = ∫ δ (τ )dτ −∞ δ (t ) = du (t ) dt [email protected] 4 s > 1¬ Àª » 7e ÎÕ ∆→0 ∆→0 [email protected] 5 s > 1¬ eª » 7Õ Î (7) δ(t) s ① x(t )δ (t ) = x(0)δ (t ) @ ªΗ x» x(0) = 0 s x(t )δ (t − t0 ) = x(t0 )δ (t − t0 ) x ( t )δ ( t ) = 0 x(0)δ (t ) x(−1)δ (t + 1) : δ T (t ) = ∞ ∑ δ (t − kT ) x(t ) k =− ∞ [email protected] x(t )δ T (t ) 6 s > 1 ¬ àÕe ª » 7 Î ∞ x(t )δ T (t ) = x(t ) ∑ δ (t − kT ) k =− ∞ ② ∫ ∞ −∞ ∞ k =− ∞ = ∞ k =− ∞ ∑ x(t )δ (t − kT ) = ∑ x(kT )δ (t − kT ) ∞ x(t )δ (t − t0 )dt = ∫ x(t0 )δ (t − t0 )dt = x(t0 ) −∞ [email protected] 7 s > 1¬ X ª » 7e ÎÕ 1.2.3 1t sin(t ) Sa (t ) = t Sa (0) = lim Sa (t ) = 1 t →0 t 2 s Sa(t) s [email protected] 8 s > 1¬ Ъ » 7e ÎÕ Sa (t ) = Sa (−t ) (1) (3) ∞ (2) ∫ Sa (t )dt = π −∞ t = kπ k = ±1 ± 2 sin(πt ) 3 sin c(t ) = = Sa (πt ) πt 1.3 X 1.3.1ª 7 D Ü ‰ e»h п [email protected] u» δ[n] 1 n = 0 (1)δ [n] = 0 n ≠ 0 [email protected] 9 s > 1 ¬ @ª » 7e ÎÕ e(2)P ¸ ªz » s 1 n = n0 δ [n − n0 ] = 0 n ≠ n0 2 ¸Pz »ªe u[n] 1 n ≥ 0 (1)u[n] = 0 n < 0 (2)u[n] s δ[n] s δ [n] = u[n] − u[n − 1] [email protected] 10 s > 1¬ X ª » 7e ÎÕ u[n] = ∞ n ∑ δ [k ] u[n] = ∑ δ [n − k ] k =− ∞ 3 hPz »ª k =0 GN[n] 1 0 ≤ n ≤ N − 1 (1)GN [n] = other 0 [email protected] 11 s > 1 ¬ ˜e ª » 7Õ Î (2)GN[n] s u[n] s δ[n] s GN [n] = u[n] − u[n − N] N −1 GN [ n ] = ∑ δ [ n − k ] k =0 1.3.2 p x[n] = a n a ∈ C w 1è@ eª » x[n] = a nt x[n] = e sn s = σ + jω a∈R [email protected] 12 s > 1¬ eª » 7Õ Î 2♦ »ª* ~S (1)ðA x[n] = e sn s = jω x[n] = e jω n e jω n = cos(ωn) + j sin(ωn) 3π x1 (t ) = sin(t ) x2 (t ) = sin t 7 3π x1[n] = sin( n) x2 [n] = sin n@ ~ª » ♦ 7 [email protected] 13 s > 1 ¬ (e ª » 7Õ Î t x1 (t )t x1 (t ) = x1 (t + 2π )t x1[n] = x1[n + 2π ] N x1[n]T ªu » eª T » u T1 = 2π x1[e ª ]T nu » [email protected] 14 s > 1¬ eª » 7Õ Î 3π x2 (t ) = sin 7 t t 14 x2 (t ) = x2 t + t 3 3π x2 [n] = sin n 7 14 x2 [ n ] = x2 n + 3 14 3 È sin(ω 0t ) sin(ω 0 n)(ª} » @ 14 14 T2 = 3 x2 [ n ] N 2 = 14 2π T= ω0 KÈ ω@ eª} 0( » [email protected] 15 s > 1¬ eª º 7Õ Î sin(ω 0 @¸ªe n»v ) : sin(ω 0 n)÷ @ vªe » sin(ω 0 n) = sin ω 0 (n + N ) = sin(ω 0 n + ω 0 N ) [email protected] 16 s > 1¬ eª » 7Õ Î 2π N =( ω0 k ω 0 N = 2kπ ) e jωª0 nH »P º 1 sin(ω 0 n) sin(ω 0 n) (2) cos(ωen» zΗ 0 ª )P eª zΗ »P ω 0 = 0t cos(ω 0t ) cos(ω 0 n) = 1 ω 0 = 2kπ º 1 cos(ω 0 n) = 1 ω0 = π 2 cos(ω 0 n) ω0 = π ωª 0»z Η eP t 1 4 cos(ω 0 n) = (−1) n [email protected] eª zΗ » 2P 17 s > 1 ¬ •e ª » 7Õ Î ω 0 = (2k − 1)π cos(ω 0 n) = (−1) n À ω0 π ÖÀ ω0 π (3) À ÖÀ HÐ 2π ϕ k [ n] = e k = 0 ± 1 ± 2 ω0 = N 1( ) ϕ k [ n] = ϕ k [ n + N ] jkω 0 n ϕ k [n + N ] = e jkω 0 ( n + N ) = e j ( kω 0 n + 2 kπ ) = e jkω 0n = ϕ k [n] t 2t ϕ k [n]t ϕ k [n] = ϕ kt N [n] Nˆ@ | eª » [email protected] 18 s > 1 ¬ •e ª » 7Õ Î ϕ 0 [n] = 1 ϕ N [n] = e jNω 0 n = e j 2π n = 1 ϕ1[n] = e jω 0 n ϕ N +1[n] = e j ( N +1)ω 0 n = e j ( 2π n +ω 0 n ) = ϕ1[n] 3( ϕ 0 [n] ~ ϕ N −1[n]|» ª ) ϕ k [ n] ϕ l [ n] N −1 ϕ k [n]ϕ l∗ [n] = 0 ∑ n =0 N −1 N −1 N −1 n =0 n =0 n =0 ϕ k [n]ϕ l∗ [n] = ∑ e jkω 0 n e − jlω 0 n = ∑ e j ( k −l )ω 0 n ∑ DFS x[n] N x[n] = 1 − e j ( k − l )ω 0 N = =0 j ( k −l )ω 0 1− e ∑ a ϕ [ n] k = <N > [email protected] k k 19 s > 1 ¬ ˜e ª º 7Õ Î e ª ‹¸ » P25 s 1.1(a)(b)(c)(d)(e) P26 s 1.2(1)(2)(3)(4) (5) P26 s 1.3(a)(b)(c)(d) P27 s 1.10(1)(2)(3)(4)(5) P27 s 1.1 1 P27 s 1.16(1)(2) [email protected] 20 ...
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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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