  The Bopp's shifts will be generalized through symplectic formalism. A special
procedure, like a "diagonalization", which drives the completely deformed
symplectic matrix to the standard symplectic form was found as suggested by
Faddeev-Jackiw. Consequently, the correspondent transformation matrix guides
the mapping from commutative to noncommutative (NC) phase-space coordinates.
The Bopp's shifts may be directly generalized from this mapping. In this
context, all the NC and scale parameters, introduced into the brackets, will be
lifted to the Hamiltonian. Well known results, obtained using $\star$-product,
will be reproduced without to consider that the NC parameters are small$(<<1)$.
Besides, it will be shown that different choices for NC algebra among the
symplectic variables generates distinct dynamical systems, which they may not
even connect with each other, and that some of them can preserve, break or
restore the symmetry of the system. Further, we will also discuss the charge
and mass rescaling in a simple model.
