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

${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space