  We discuss a new phase space method for the computation of quantum
expectation values in the high frequency regime. Instead of representing a
wavefunction by its Wigner function, which typically attains negative values,
we define a new phase space density by adding a first-order Hermite spectrogram
term as a correction to the Husimi function. The new phase space density yields
accurate approximations of the quantum expectation values as well as allows
numerical sampling from non-negative densities. We illustrate the new method by
numerical experiments in up to $128$ dimensions.
