Fungsi Heaviside step: Béda antarrépisi

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Baris ka-1:
<div style="float:right;margin-left:5px;text-align:center;padding-left:10px">[[Gambar:HeavisideStepFunction.png|The Heaviside step function]]</div>
 
'''Fungsi Heaviside step''', ngaran nu dipakedipaké keur ngahargaan ka [[Oliver Heaviside]], nyaetanyaéta a [[Fungsi (matematik)|fungsi]] [[continuous|diskontinyu]] numana nileyna nyaetanyaéta [[zero|nol]] keur asupan negatip sarta [[one|hiji]] keur nu sejenna:
:<math>H(x)=\left\{\begin{matrix} 0 : x < 0 \\ 1 : x \ge 0 \end{matrix}\right. </math>
 
Baris ka-8:
It is the [[cumulative distribution function]] of a [[variabel acak]] which is [[almost surely]] 0. (See [[constant random variable]].)
 
The Heaviside function is the integral of the [[Dirac delta function]]. The value of H(0) is of very little importance, since the function is often used within an [[integration|integral]]. Some writers give H(0) = 0, some H(0) = 1. H(0) = 0.5 is often used, since it maximizes the [[symmetry]] of the function. This makesmakés the definition:
 
:<math>H(x)=\left\{\begin{matrix} 0 : x < 0 \\ \frac{1}{2} : x = 0 \\ 1 : x > 0 \end{matrix}\right. </math>
Baris ka-18:
where ''c'' is a positive offset in the ''x''-dimension of the transition from 0 to 1. In other words, ''H''<sub>3</sub>(''x'') = ''H''(''x'' − 3) would be zero until ''x'' = 3, and would transition to 1 for ''x'' > 3. The meaning of the subscript should be given in context.
 
The question of the [[Fourier transform]] of H is an interesting example for the theory of [[distribution]]s. It is often stated that it is 1/x, up to a [[normalizing constant]]. But near x=0 that cannot be justified: the definition must be given in terms of ''[[Cauchy principal value|principal value]]'' limit, and the transform isn't to be treatedtréated simply as a function. The corresponding [[convolution|convolution operator]] is the ''[[Hilbert transform]]''.
 
Often an integral representation of the step function is useful,
Baris ka-24:
e^{-i\tau x},</math>
in the limit <math>\epsilon\to 0</math>.
 
 
== Related topics ==