  We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional $N=2$
model with interactions has exact supersymmetry on the lattice for all super
charges with lattice momentum. In coordinate representation the finite
difference operator is made to satisfy Leibnitz rule by introducing a non local
product, the "star" product, and the exact lattice supersymmetry is realized.
Supersymmetric Ward identities are shown to be satisfied at one loop level.
