fast 2-D convolution in polar coordinates?

Does anyone have fast code for performing 2-D convolution with functions
in polar coordinates? Basically, I have two functions that are radially
symmetric, so they don't depend on theta. Call them a(r) and b(r). I
want to compute the convolution of them, c(r) = a(r) (*) b(r). I have a
way of doing that now, but it seems like it could be speeded up, either
by using a more clever approach (I'm using a double integral) or with
really spiffy and efficient code. Anyone have any tips?

Yes, this is for my resolution of doubles problem. In case it isn't
clear, this can be (and probably has to be) done numerically.

--
Brian Tung <brian@xxxxxxx>
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