  We prove a formula expressing the gradient of the phase function of a
function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency
moment of the Wigner distribution for fixed time. The formula holds when $f$ is
the Fourier transform of a distribution of compact support, or when $f$ belongs
to a Sobolev space $H^{d/2+1+\epsilon}(\mathbb R^d)$ where $\epsilon>0$. The
restriction of the Wigner distribution to fixed time is well defined provided a
certain condition on its wave front set is satisfied. Therefore we first study
the wave front set of the Wigner distribution of a tempered distribution.
