奇异函数（英语：singularity function）是一类含有奇异点的不连续函数（在奇异点不连续），其在数学领域里的名称为广义函数或分布。这些函数以角括号标记，形如 ，其中n为整数。而“”则被称为奇异括号。奇异函数的定义为：

其中，表示狄拉克δ函数，即单位脉冲。的一次导数则被称为单位偶。为单位阶跃函数：x<0 时 H(x)=0，而 x>0 时 H(x)=1。H(0)的值则按具体的约定而定。需要注意的是只有n=0时H(0)的值才有影响。则称为斜坡函数。

Singularity functions are a class of discontinuous functions that contain singularities, i.e. they are discontinuous at their singular points. Singularity functions have been heavily studied in the field of mathematics under the alternative names of generalized functions and distribution theory. The functions are notated with brackets, as where n is an integer. The "" are often referred to as singularity brackets . The functions are defined as: