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冲激偶

ImpulsePairEven

偶冲激偶是 傅里叶变换 cos(pik)，

AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2).
(1)

它满足

AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)*f(x)=1/2f(x+1/2)+1/2f(x-1/2),
(2)

其中 * 表示 卷积，并且

int_(-infty)^inftyAdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)dx=1.
(3)
ImpulsePairOdd

奇冲激偶是 傅里叶变换 isin(pis)，

AdjustmentBox[I, BoxMargins -> {{0.101266, -0.101266}, {0.375, -0.375}}, BoxBaselineShift -> -0.375]AdjustmentBox[I, BoxMargins -> {{0, 0}, {-0.25, 0.25}}, BoxBaselineShift -> 0.25](x)=1/2delta(x+1/2)-1/2delta(x-1/2).
(4)

使用 Wolfram|Alpha 探索

引用为

Weisstein, Eric W. “冲激偶。” 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/ImpulsePair.html

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