distribution functions in light of the uncertainty principle

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty principle. on the other hand the wigner distribution function while becoming negative incertain regions of the phase space do not violate the uncertainty principle.