Vychislitelny_praktikum
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7 |
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6 |
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Vector_τmax |
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j |
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5 |
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4 |
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30.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1 |
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0.5+0.1 j |
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18. Построить зависимость интервала дискретизации от порядка функции при заданном параметре масштаба.
При параметре масштаба γ = 1, k = 0..5.
0.40.126
Vector_Δτ := 0.06 0.0340.022
0.015
0.4 |
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0.32 |
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0.24 |
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Vector_Δτj |
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0.16 |
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0.08 |
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1 |
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3 |
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j |
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183
Приложение 7
ЧАСТОТНЫЕ ХАРАКТЕРИСТИКИ ОРТОГОНАЛЬНЫХ ФУНКЦИЙ
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Частотные характеристики ортогональных функций Лагерра |
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k = 0, 2, 4 |
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k = 1, 3, 5 |
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0 |
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0.2 |
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1.24 |
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0.4 |
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0.68 |
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ImWk(ω,k) |
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ImWk(ω,k) |
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0.6 |
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0.12 |
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0.8 |
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0.44 |
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1 |
0 |
0.4 |
0.8 |
1.2 |
1.6 |
2 |
1 |
2 |
1.24 |
0.48 |
0.28 |
1.04 |
1.8 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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1.25 |
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2 |
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0.6 |
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1.2 |
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0.05 |
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0.4 |
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ImWk(ω,k) |
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ImWk(ω,k) |
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0.7 |
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0.4 |
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1.35 |
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1.2 |
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21.95 |
1.17 |
0.39 |
0.39 |
1.17 |
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2 |
2 |
1.2 |
0.4 |
0.4 |
1.2 |
2 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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2 |
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2 |
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1 |
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1 |
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ImWk(ω,k) 0 |
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ImWk(ω,k) 0 |
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1 |
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1 |
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2 |
2 |
1 |
0 |
1 |
2 |
2 |
2 |
1 |
0 |
1 |
2 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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184
Продолжение приложения 7
Частотные характеристики ортогональных функций Сонина-Лагерра (α = 2)
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k = 0, 2, 4 |
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k = 1, 3, 5 |
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0 |
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0.2 |
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0.008 |
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0.4 |
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0.14 |
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ImWk(ω, k) |
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ImWk(ω, k) |
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0.6 |
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0.3 |
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0.8 |
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0.45 |
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1 |
0 |
0.4 |
0.8 |
1.2 |
1.6 |
2 |
0.6 |
0 |
0.21 |
0.42 |
0.63 |
0.84 |
1.05 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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0.05 |
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0.06 |
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0.044 |
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0.017 |
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0.14 |
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0.093 |
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ImWk(ω, k) |
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ImWk(ω, k) |
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0.23 |
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0.17 |
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0.33 |
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0.25 |
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0.42 0 |
0.14 |
0.29 |
0.43 |
0.58 |
0.72 |
0.32 0 |
0.11 |
0.22 |
0.34 |
0.45 |
0.56 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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0.023 |
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0.03 |
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0.028 |
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0.09 |
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0.078 |
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ImWk(ω, k) |
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ImWk(ω, k) |
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0.15 |
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0.13 |
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0.21 |
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0.18 |
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0.27 |
0 |
0.092 |
0.18 |
0.28 |
0.37 |
0.46 |
0.23 |
0 |
0.078 |
0.16 |
0.23 |
0.31 |
0.39 |
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ReWk(ω,k) |
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ReWk(ω,k) |
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186
Продолжение приложения 7
Частотные характеристики ортогональных функций Якоби (α = 1, β = 0)
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k = 0, 2, 4 |
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k = 1, 3, 5 |
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0 |
0.25 |
0.5 |
0.75 |
1 |
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0.2 |
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0.15 |
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0.5 |
0.22 |
0.05 |
0.33 |
0.6 |
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ImWk_0(ω,k) 0.3 |
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ImWk_0(ω,k) |
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0.2 |
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0.45 |
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0.4 |
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0.6 |
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0.6 |
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ReWk_0(ω, k) |
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ReWk_0(ω,k) |
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0.4 |
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0.27 |
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0.2 |
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0.1 |
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ImWk_0(ω,k) |
0.16 |
0.025 |
0.21 |
ImWk_0(ω,k) |
0.25 |
0.11 0.065 0.025 |
0.16 |
0.3 |
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0.35 |
0.4 |
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0.2 |
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0.23 |
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0.4 |
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0.4 |
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ReWk_0(ω,k) |
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ReWk_0(ω,k) |
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0.2 |
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0.2 |
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0.1 |
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0.1 |
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ImWk_0(ω,k) |
0.13 |
0 |
0.13 |
ImWk_0(ω, k) |
0.2 |
0.1 |
0 |
0.1 |
0.2 |
0.25 |
0.25 |
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0.1 |
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0.1 |
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0.2 |
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0.2 |
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ReWk_0(ω,k) |
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ReWk_0(ω, k) |
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188
Продолжение приложения 7
Частотные характеристики ортогональных функций Якоби (α = 0, β = 1)
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k = 0, 2, 4 |
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k = 1, 3, 5 |
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0 |
0.25 |
0.5 |
0.75 |
1 |
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0.13 |
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0.15 |
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0.063 |
ImWk_1(ω,k) |
0.3 |
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ImWk_1(ω,k) |
0.25 |
0.19 |
0.13 |
0.063 |
0 |
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0.45 |
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0.063 |
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0.6 |
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0.13 |
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ReWk_1(ω, k) |
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ReWk_1(ω,k) |
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0.06 |
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0.035 |
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0.029 |
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0.018 |
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ImWk_1(ω,k) 0.0025 0 |
0.03 |
0.06 |
0.09 |
0.12 |
ImWk_1(ω,k) |
0 |
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0.034 |
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0.018 |
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0.065 |
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0.035 |
0.049 |
0.033 |
0.016 |
0 |
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0.065 |
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ReWk_1(ω,k) |
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ReWk_1(ω,k) |
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0.025 |
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0.015 |
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0.015 |
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0.013 |
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0.0075 |
ImWk_1(ω,k) |
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ImWk_1(ω, k) |
0.03 |
0.0225 |
0.015 |
0.0075 |
0 |
0 |
0.01 |
0.02 |
0.03 |
0.04 |
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0.013 |
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0.0075 |
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− 0.015 |
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0.015 |
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0.025 |
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ReWk_1(ω,k) |
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− 0.03 |
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ReWk_1(ω,k) |
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0 |
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190
Продолжение приложения 7
Частотные характеристики ортогональных функций Якоби (α = −0,5, β = 0)
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k = 0, 2, 4 |
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k = 1, 3, 5 |
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0 |
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0.14 |
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0.25 |
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0.00375 |
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ImWk_0(ω,k) |
0.5 |
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ImWk_0(ω,k) |
0.15 |
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0.75 |
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0.3 |
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1 |
0 |
0.5 |
1 |
1.5 |
2 |
0.450.5 |
0.24 |
0.025 |
0.29 |
0.55 |
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ReWk_0(ω,k) |
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ReWk_0(ω,k) |
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0.25 |
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0.18 |
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0.13 |
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0.09 |
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ImWk_0(ω,k) 0 |
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ImWk_0(ω,k) 0 |
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0.13 |
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0.09 |
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0.25 |
0.12 |
0 |
0.12 |
0.24 |
0.18 |
0.09 |
0 |
0.09 |
0.18 |
0.24 |
0.18 |
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ReWk_0(ω,k) |
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ReWk_0(ω,k) |
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0.12 |
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0.1 |
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0.06 |
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0.05 |
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ImWk_0(ω,k) 0 |
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ImWk_0(ω,k) 0 |
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0.06 |
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0.05 |
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0.12 |
0.06 |
0 |
0.06 |
0.12 |
0.1 |
0.05 |
0 |
0.05 |
0.1 |
0.12 |
0.1 |
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ReWk_0(ω,k) |
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ReWk_0(ω,k) |
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192