| u(t)=0 (t＜0) =1 (t≧0)  (Lapalace変換) |
[Mathmatica] Heavicide(t) |
| [wxMaxima] unit_step(t)  |
[wxMaxima] plot2d(unit_step(x),[x,-1,2],[y,-.5,1.5]); unit_step(0); 0 limit(unit_step(t),t,0,plus); 1 |
| u(t)=0 (t＜0) =1/2 (t=0) = 1 (t＞0)  (Fourier級数展開) |
[Maple10] Heavicide(t) |
| csgn(t)=0 (t=0) =1 (t＞0) =-1 (t＜0) |
[Maple10] |
| unit_step(t)=0(x≦0) =1(x＞0) (Laplace変換) |
[Maxima] load(orthopoly); unit_step(t) laplace(unit_step(t),t,s) |
| signum(t)=0 (t=0) =1 (t＞0) =-1 (t＜0) |
[Maxima] load(orthopoly); signum(t) |
| (1+signum(t))/2=0 (t＜0) =1/2 (t=0) = 1 (t＞0) (Fourier級数展開) |
[Maxima] load(orthopoly); (1+signum(t))/2 |
パルス波形
| Unit Step関数 y=u (t) の プロット [Maple10]使用 csgn(t)=1 (t>0) =0 (t=0) =-1(t<0) |
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| 遅延Unit Step関数 y=u (t-1) の プロット [Maple10]使用 csgn(t)=1 (t>1) =0 (t=1) =-1(t<1) |
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| 矩形波 周期T=4 振幅=±1 f (t)=-1(-2≦t＜-1) = 1(-1≦t≦ 1) =-1( 1≦t＜ 2) [Maple10]使用 csgn(t)=1 (t>0) =0 (t=0) =-1(t<0) |
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| 全波整流sin波 周期T=1,振幅=1 y = sin(πt) ( 0≦t＜0.5) = -sin(πt) (-0.5≦t＜0) [Maple10]使用 csgn(t)=1 (t>0) =0 (t=0) =-1(t<0) |
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| 全波整流cos波 周期T=1,振幅=1 y = cos(πt) ( 0≦|t|＜0.5) = -cos(πt) (-0.5≦|t| ) [Maple10]使用 csgn(t)=1 (t>0) =0 (t=0) =-1(t<0) |
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δ関数(delta function) δ(t)
| δ(t)=0 (t＜0, t＞0) =∞ (t=0) |
∫[-∞→∞] δ(t)dt=1 ∫[-∞→∞] ｆ(t)δ(t-a)dt=f(a) |
| [Mathematica] |
Dirac(t) |
| [Maple10] |
Dirac(t) |