heaviside step function

heaviside step function:阶跃函数

The function is used in the mathematics of control theory and signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely. It was named after the English polymath Oliver Heaviside.

It is the cumulative distribution function of a random variable which is almost surely 0. (See constant random variable.)

The Heaviside function is the integral of the Dirac delta function: H′ = δ. This is sometimes written as

H(x) = \int_{-\infty}^x { \delta(t)} \mathrm{d}t

although this expansion may not hold (or even make sense) for x = 0, depending on which formalism one uses to give meaning to integrals involving δ.

example：

H[n]=\begin{cases} 0, & n < 0 \\ 1, & n \ge 0 \end{cases} 

posted on 2010-09-06 10:14  Rochen  阅读(1259)  评论(0)  编辑  收藏  举报

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