  In this paper we generalize the concept of Wigner function in the case of
quantum mechanics with a minimum length scale arising due to the application of
a generalized uncertainty principle (GUP). We present the phase space
formulation of such theories following GUP and show that the Weyl transform and
the Wigner function does satisfy some of their known properties in standard
quantum mechanics. We utilise the generalized Wigner function to calculate the
phase space average of the Hamiltonian of a quantum harmonic oscillator
satisfying deformed Heisenberg algebra. It is also shown that averages of
certain quantum mechanical operators in such theories may restrict the value of
the deformation parameter specifying the degree of deformation of Heisenberg
algebra. All the results presented are for pure states. The results can be
generalized for mixed states.
