MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Convolution and Integration of Top Hat Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33196] Convolution and Integration of Top Hat Functions
  • From: Roger Jones <rmj at SLAC.Stanford.EDU>
  • Date: Thu, 7 Mar 2002 02:24:08 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

The first convolution of two Top Hat  functions is the triangle
function.  This does not come out explicitly in Mathematica 4.1 as can
be seen from the below example.  The first part of the IF statement is
indeed the correct solution but the second option to the IF is not
required.   Obviously this can be coded to force only the first part of
the IF condition to be displayed but I would have expected this to be
automatic.

I also, note that in Mathematica 3.0 this was not the case as only the
first part of the if conditional was given as the solution.

Thanks!

-Roger Jones


Clear[II];
(* Define "Top Hat" function *)
 Clear[II];
  II[xx_] = UnitStep[1\/2 + xx] - UnitStep[xx - 1\/2];

(* Convolve *)
f[yy_]=Integrate[II[xx]  II[yy-xx],{xx,-Infinity,Infinity}]

   1                            1
If[- - yy > -Infinity && yy < -(-) &&
   2                            2

        1
   yy < -, (-1 + yy) UnitStep[-1 + yy] -
        2

   2 yy UnitStep[yy] +

   (1 + yy) UnitStep[1 + yy],

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

               1
      UnitStep[- + xx])
               2

                 1
    (-UnitStep[-(-) - xx + yy] +
                 2

               1
      UnitStep[- - xx + yy]),
               2

   {xx, -Infinity, Infinity}]]




  • Prev by Date: Re: Creating pdf on Mac OSX
  • Next by Date: Re: How to transform x axis on ListPlot?
  • Previous by thread: Stokes integral transformation with Mathematica ?
  • Next by thread: Re: Re: integral transform definition