  In this paper extensions of the classical Fourier, fractional Fourier and
Radon transforms to superspace are studied. Previously, a Fourier transform in
superspace was already studied, but with a different kernel. In this work, the
fermionic part of the Fourier kernel has a natural symplectic structure,
derived using a Clifford analysis approach. Several basic properties of these
three transforms are studied. Using suitable generalizations of the Hermite
polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer
polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007)
10441-10456]) an eigenfunction basis for the Fourier transform is constructed.
