  Non-Commutative (NC) effects in planar quantum mechanics are investigated. We
have constructed a {\it{Master}} model for a noncommutative harmonic oscillator
by embedding it in an extended space, following the Batalin-Tyutin \cite{bt}
prescription. Different gauge choices lead to distinct NC structures, such as
NC coordinates, NC momenta or noncommutativity of a more general kind. In the
present framework, all of these can be studied in a unified and systematic
manner. Thus the dual nature of theories having different forms of
noncommutativity is also revealed.
