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.