“Heaviside Step Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Heaviside Step Function

释义

Heaviside Step Function

A discontinuous ``step'' function, also called the Unit Step, and defined by

(1)

It is related to the Boxcar Function. The Derivative is given by

(2)

where

is the Delta Function, and the step function is related to theRamp Function

(3)

Bracewell (1965) gives many identities, some of which include the following. Letting denote the Convolution,

(4)

Additional identities are

(7)


			(8)

The step function obeys the integral identities

			(9)
			(10)

(11)

The Heaviside step function can be defined by the following limits,

where

is the Erfc function,

is the Sine Integral,

is theSinc Function, and

is the one-argument Triangle Function and

The Fourier Transform of the Heaviside step function is given by

(19)

where

is the Delta Function.

See also Boxcar Function, Delta Function,Fourier Transform--Heaviside Step Function,Ramp Function, Ramp Function, Rectangle Function, Square Wave

References

Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, 1965.

Spanier, J. and Oldham, K. B. ``The Unit-Step and Related Functions.'' Ch. 8 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 63-69, 1987.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。