Integrating Unit Step Functions (Convolution)

• To: mathgroup at smc.vnet.net
• Subject: [mg22926] Integrating Unit Step Functions (Convolution)
• From: Roger Jones <rmj at slac.stanford.edu>
• Date: Thu, 6 Apr 2000 02:04:43 -0400 (EDT)
• Organization: Stanford Linear Accelerator Center
• Sender: owner-wri-mathgroup at wolfram.com

```In mathematica 3.1 the convolution of II[x], (the "Top Hat" function)
with itself gives
(the Triangle function):

In[]=Simplify[Integrate[ II[u] II[x-u],{u,-Infinity,Infinity}]=
Out[]=(-1 + x) UnitStep[-1 + x] - 2 x UnitStep[x] +  (1 + x) UnitStep[1
+ x]

whereas Mathematica 4.0 gives:

Out[]=
1
If[- + x < 0, (-1 + x) UnitStep[-1 + x] -
2

2 x UnitStep[x] + (1 + x) UnitStep[1 + x],

1
Integrate[(-UnitStep[-(-) + u] +
2

1
UnitStep[- + u])
2

1                      1
(-UnitStep[-(-) - u + x] + UnitStep[- - u + x])
2                      2

, {u, -Infinity, Infinity}]]

Is there some bug in Mathematica 4.0 or perhaps there is some options I
should apply for this integral?
By hand, Mathematica 3.1 gives the correct result.

-Roger Jones

```

• Prev by Date: contour plot
• Next by Date: Q: Axes on top of graphics primitives?
• Previous by thread: contour plot
• Next by thread: Q: Axes on top of graphics primitives?