We study the noncommutative superspace of arbitrary dimensions in a
systematic way. Superfield theories on a noncommutative superspace can be
formulated in two folds, through the star product formalism and in terms of the
supermatrices. We elaborate the duality between them by constructing the
isomorphism explicitly and relating the superspace integrations of the star
product Lagrangian or the superpotential to the traces of the supermatrices. We
show there exists an interesting fine tuned commutative limit where the duality
can be still maintained. Namely on the commutative superspace too, there exists
a supermatrix model description for the superfield theory. We interpret the
result in the context of the wave particle duality. The dual particles for the
superfields in even and odd spacetime dimensions are D-instantons and D0-branes
respectively to be consistent with the T-duality.Comment: 1+16 pages, no figure; expanded version, references added; Convention
for Clifford algebra improve