Curious about something. In Maple 10 I was able to find the inverse Fourier transform of a product of transforms (a linear filter actually) by definition.  For example, Maple 10 would evaluate:

1/sqrt(2*Pi)*int(LF*exp(I*lambda*t),lambda=-infinity..infinity) where LF is was a product of two Fourier transforms.

Maple 11 on the other hand will not evaluate the integral and I am left having to use:

with(inttrans): sqrt(2*Pi)*invfourier(LF,lambda,t);