| dbo:abstract |
In mathematics, the unit doublet is the derivative of the Dirac delta function. It can be used to differentiate signals in electrical engineering: If u1 is the unit doublet, then where is the convolution operator. The function is zero for all values except zero, where its behaviour is interesting. Its integral over any interval enclosing zero is zero. However, the integral of its absolute value over any region enclosing zero goes to infinity. The function can be thought of as the limiting case of two rectangles, one in the second quadrant, and the other in the fourth. The length of each rectangle is k, whereas their breadth is 1/k2, where k tends to zero. (en) 在数学中，单位偶（unit doublet）是狄拉克δ函数的导数。其可用于对信号进行微分运算。假设u1是单位偶，则 其中 * 表示卷积符号。 单位偶在零以外的点的值都为零。其在任意包含零点的区间的积分都为零。而在任意包含零点的区间对其绝对值进行积分的话，得到的结果为无穷大。此函数可看作是两个矩形的极限情形，其中一个矩形位于第二象限，另一个位于第四象限。每个矩形的宽度为k、长度为 1/k2，而k则趋向于零。 (zh) |
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dbc:Generalized_functions |
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| rdfs:comment |
在数学中，单位偶（unit doublet）是狄拉克δ函数的导数。其可用于对信号进行微分运算。假设u1是单位偶，则 其中 * 表示卷积符号。 单位偶在零以外的点的值都为零。其在任意包含零点的区间的积分都为零。而在任意包含零点的区间对其绝对值进行积分的话，得到的结果为无穷大。此函数可看作是两个矩形的极限情形，其中一个矩形位于第二象限，另一个位于第四象限。每个矩形的宽度为k、长度为 1/k2，而k则趋向于零。 (zh) In mathematics, the unit doublet is the derivative of the Dirac delta function. It can be used to differentiate signals in electrical engineering: If u1 is the unit doublet, then where is the convolution operator. (en) |
| rdfs:label |
Unit doublet (en) 单位偶 (zh) |
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