Vychislitelny_praktikum
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Продолжение приложения 8 |
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Частотные характеристики ортогональных фильтров 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 |
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2 |
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0.4 |
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0.4 |
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0.8 |
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1.2 |
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Im(W11(k,ω,γ)) |
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Im(W11(k,ω,γ)) |
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1.2 |
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2.8 |
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1.6 |
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4.4 |
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2 1 |
0.2 |
0.6 |
1.4 |
2.2 |
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6 4 |
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Re(W11(k,ω,γ)) |
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Re(W11(k,ω,γ)) |
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2 |
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Im(W11(k,ω,γ)) |
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Im(W11(k,ω,γ)) |
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10 10 |
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Re(W11(k,ω,γ)) |
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Re(W11(k,ω,γ)) |
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2 |
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4 |
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Im(W11(k,ω,γ)) |
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Im(W11(k,ω,γ)) |
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20 10 |
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Re(W11(k,ω,γ)) |
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Re(W11(k,ω,γ)) |
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203
Продолжение приложения 8
Частотные характеристики ортогональных фильтров Якоби (α =0, β = 2)
k = 0, 2, 4 |
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k = 1, 3, 5 |
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1 |
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5 |
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0.2 |
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2 |
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0.6 |
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1 |
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Im(W12(k,ω,γ)) |
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Im(W12(k,ω,γ)) |
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1.4 |
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4 |
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2.2 |
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3 1 |
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2 |
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10 10 |
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Re(W12(k,ω,γ)) |
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Re(W12(k,ω,γ)) |
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4 |
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Im(W12(k,ω,γ)) |
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Im(W12(k,ω,γ)) |
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4 |
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20 20 |
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40 |
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Re(W12(k,ω,γ)) |
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Re(W12(k,ω,γ)) |
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40 |
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50 |
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Im(W12(k,ω,γ)) |
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Im(W12(k,ω,γ)) |
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40 40 |
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50 |
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Re(W12(k,ω,γ)) |
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Re(W12(k,ω,γ)) |
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204
Продолжение приложения 8
Частотные характеристики ортогональных фильтров 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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1 |
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0.2 |
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0.4 |
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0.4 |
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0.2 |
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Im(W6(k,ω,γ)) |
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Im(W6(k,ω,γ)) |
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0.6 |
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0.8 |
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0.8 |
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1.4 |
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1 0 |
0.4 |
0.8 |
1.2 |
1.6 |
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2 |
1.2 |
0.4 |
0.4 |
1.2 |
2 |
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Re(W6(k,ω,γ)) |
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Re(W6(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W6(k,ω,γ)) |
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Im(W6(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
2 |
2 |
2 |
1.2 |
0.4 |
0.4 |
1.2 |
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Re(W6(k,ω,γ)) |
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Re(W6(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W6(k,ω,γ)) |
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Im(W6(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
2 |
2 |
2 |
1.2 |
0.4 |
0.4 |
1.2 |
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Re(W6(k,ω,γ)) |
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Re(W6(k,ω,γ)) |
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205
Продолжение приложения 8
Частотные характеристики ортогональных фильтров 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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1 |
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0.2 |
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0.4 |
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0.4 |
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0.2 |
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Im(W7(k,ω,γ)) |
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Im(W7(k,ω,γ)) |
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0.6 |
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0.8 |
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0.8 |
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1.4 |
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1 0 |
0.4 |
0.8 |
1.2 |
1.6 |
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1.2 |
0.4 |
0.4 |
1.2 |
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Re(W7(k,ω,γ)) |
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Re(W7(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W7(k,ω,γ)) |
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Im(W7(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
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1.2 |
0.4 |
0.4 |
1.2 |
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Re(W7(k,ω,γ)) |
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Re(W7(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W7(k,ω,γ)) |
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Im(W7(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
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1.2 |
0.4 |
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1.2 |
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Re(W7(k,ω,γ)) |
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Re(W7(k,ω,γ)) |
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206
Продолжение приложения 8
Частотные характеристики ортогональных фильтров Дирихле
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0 |
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2 |
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0.2 |
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1.4 |
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0.4 |
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0.8 |
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Im(W5(k,ω,γ)) |
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Im(W5(k,ω,γ)) |
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0.6 |
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0.2 |
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0.8 |
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0.4 |
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1 0 |
0.4 |
0.8 |
1.2 |
1.6 |
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1.2 |
0.4 |
0.4 |
1.2 |
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Re(W5(k,ω,γ)) |
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Re(W5(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W5(k,ω,γ)) |
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Im(W5(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
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1.2 |
0.4 |
0.4 |
1.2 |
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Re(W5(k,ω,γ)) |
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Re(W5(k,ω,γ)) |
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2 |
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2 |
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1.2 |
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1.2 |
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0.4 |
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0.4 |
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Im(W5(k,ω,γ)) |
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Im(W5(k,ω,γ)) |
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0.4 |
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0.4 |
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1.2 |
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1.2 |
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2 2 |
1.2 |
0.4 |
0.4 |
1.2 |
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1.2 |
0.4 |
0.4 |
1.2 |
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Re(W5(k,ω,γ)) |
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Re(W5(k,ω,γ)) |
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1.5 |
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ReW(0,ω) 1.1 |
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ReW(1,ω) |
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ReW(2,ω) 0.7 |
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ReW(3,ω) 0.3 |
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ReW(4,ω) |
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− 0.1 |
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− 0.50 |
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ω |
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0.4 |
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ImW(0 |
,ω) |
0.2 |
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ImW(1 |
,ω) |
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ImW(2 |
,ω) |
0 |
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ImW(3 |
,ω)− 0.2 |
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ImW(4,ω)
− 0.4
− 0.6 |
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ω |
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1.5
MoW(0,ω)1.2
MoW(1,ω)
MoW(2,ω)0.9
MoW(3,ω)0.6
MoW(4,ω)
0.3
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ω |
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π |
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ΦW(0,ω) |
1.2 |
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ΦW(1,ω)
ΦW(2,ω) 0.4
ΦW(3,ω)− 0.4
ΦW(4,ω)
− 1.2 |
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π |
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− |
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− 2 |
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50 |
ω
2. Построить зависимость квадрата модуля частотной характеристики ортогонального фильтра от порядка m; m = 0 - 4, γ = const.
MoWf (m,ω) := |
4 (m + 1)2 γ2 |
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(m + 1)2 γ2 + ω2 |
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MoWf (0,ω)3.2 |
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MoWf (1 |
,ω) |
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MoWf (2 |
,ω)2.4 |
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MoWf (3 |
,ω)1.6 |
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MoWf (4 |
,ω) |
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0.8 |
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25 |
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ω |
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3. Построить зависимость квадрата модуля частотной характеристики ортогонального фильтра от параметра γ; m = const.
m := 3 |
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MoWf (γ,ω1) := |
4 (m + 1)2 γ2 |
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(m + 1)2 γ2 + ω12 |
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210
CreateMesh (MoWf )
4. Построить зависимость полосы пропускания ортогонального фильтра m - ого порядка от параметра γ; m = 0 - 4.
ω |
c |
(m,γ) := π γ (m + 1) |
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200 |
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ωc(0,γ1 )160 |
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ωc(1,γ1 ) |
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ωc(2 |
120 |
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,γ1 ) |
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ωc(3 |
,γ1 ) 80 |
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ωc(4 |
,γ1 ) |
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40 |
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0 |
0 |
5 |
10 |
15 |
20 |
25 |
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γ1 |
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211
Приложение 10
АНАЛИТИЧЕСКИЕ ВЫРАЖЕНИЯ ДЛЯ ВЫЧИСЛЕНИЯ КОЭФФИЦИЕНТОВ РАЗЛОЖЕНИЯ
Модель ρx (τ )= e−λ τ
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Таблица П 10.1 |
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ψk (τ ,γ / α) |
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βk |
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1 |
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P(−1 2,0) (τ,γ) |
γ (4k +1)∑k |
Cks Cks+−s1−/ |
12/ 2 |
(−1)s |
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(λ +γ ((4s +1)/ 2)) |
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k |
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s=0 |
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γ (4k + 3)∑k |
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(−1)s |
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1 |
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P(1 2,0 )(τ,γ) |
Cks Cks++s1+/ |
12/ 2 |
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(λ +γ ((4s + 3)/ 2)) |
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k |
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s=0 |
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2γ (2k +1)∑k |
Cks Cks+s (−1)s |
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1 |
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P( 0,0 ) (τ,γ) |
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(λ +γ (2s +1)) |
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k |
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s=0 |
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2γ (k +1)∑k |
Cks Cks++s1+1 (−1)s |
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1 |
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P( 1,0 ) (τ,γ) |
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(λ +γ (s +1)) |
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k |
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s=0 |
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2γ (2k + 3)∑k |
Cks Cks++s2+2 (−1)s |
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1 |
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P( 2,0 ) (τ,γ) |
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(λ +γ (2s + 3)) |
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k |
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s=0 |
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γ ∑Cks |
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(−γ ) |
s |
s+1 |
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Lk (τ ,γ ) |
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k |
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s=0 |
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(λ +γ / 2) |
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k |
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k −s (−γ )s (s +1) |
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(1) |
(τ ,γ ) |
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2 |
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Lk |
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γ |
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∑Ck +1 |
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(λ +γ / 2) |
s+2 |
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s=0 |
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γ 3 |
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k −s (−γ )s (s +1)(s + 2) |
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(2 ) |
(τ ,γ ) |
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Lk |
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∑Ck +2 |
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2 |
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(λ +γ / 2) |
s+3 |
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s=0 |
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212