I'm not sure how the API compares to FFTW, but if you're on Nvidia hardware the toolkit comes with the CUFFT library http://developer.nvidia.com/object/cuda_3_2_toolkit_rc.html which is tuned for their hardware.

I seem to recall needing to transfer the data to GPU memory and other things like that when I last used it, but that was prior to toolkit 2.0 IIRC.