A discontinuous ``step'' function, also called the Unit Step, and defined by
(1) |
(2) |
(3) |
Bracewell (1965) gives many identities, some of which include the following. Letting denote the Convolution,
(4) |
(5) | |||
(6) |
(7) |
(8) |
(9) | |||
(10) |
(11) |
The Heaviside step function can be defined by the following limits,
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(13) | |||
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(16) | |||
(17) | |||
(18) |
The Fourier Transform of the Heaviside step function is given by
(19) |
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.
© 1996-9 Eric W. Weisstein