  This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic
oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics
of the harmonic oscillator based on a noncanonical commutation relation
depending on the phase space coordinates. A reformulation of this deformation
is considered in terms of a $q-$deformation allowing to easily deduce the
energy spectrum of the induced deformed harmonic oscillator. Then, it is proved
that the deformed position and momentum operators admit a one-parameter family
of self-adjoint extensions. These operators engender new families of deformed
Hermite polynomials generalizing usual $q-$ Hermite polynomials. Relevant
matrix elements are computed. Finally, a $su(2)-$algebra representation of the
considered deformation is investigated and discussed.
