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Re: 2D Convolution

• To: mathgroup at smc.vnet.net
• Subject: [mg76140] Re: 2D Convolution
• From: CKWong <CKWong.P at gmail.com>
• Date: Wed, 16 May 2007 05:51:57 -0400 (EDT)
• References: <f29389$m7p$1@smc.vnet.net><f29bko$pjn$1@smc.vnet.net>

You need to re-define your Convolve like this:

Convolve[f_, g_, x_?NumberQ, y_?NumberQ] := NIntegrate[f[
    xPrime, yPrime] *g[x - xPrime,
  y - yPrime], {xPrime, -=A1=DB, =A1=DB}, {yPrime, -=A1=DB, =A1=DB}]

When calling Convolve, remember to place the kernel as the first
function, e.g.,

Convolve[Gaussian2D, SHole, 0, 0]

You can plot the convolution like this:

Plot3D[Convolve[Gaussian2D, SHole, x, y] // Evaluate, {x, -HoleSize,
      HoleSize}, {y, -HoleSize, HoleSize}]

However, this scheme is too slow for the round hole, for which case,
it's better to switch to polar coordinates so that the angular part
can be integrated by hand.