  One of the most popular time-frequency representation is certainly the Wigner
distribution. To reduce the interferences coming from its quadratic nature,
several related distributions have been proposed, among which the so-called
Born-Jordan distribution. It is well known that in the Born-Jordan distribution
the ghost frequencies are in fact damped quite well, and the noise is in
general reduced. However, the horizontal and vertical directions escape from
this general smoothing effect, so that the interferences arranged along these
directions are in general kept. Whereas these features are graphically evident
on examples and heuristically well understood in the engineering community,
there is not at present a mathematical explanation of these phenomena, valid
for general signals in L^2 and, more in general, in the space S' of temperate
distributions. In the present note we provide such a rigorous study using the
notion of wave-front set of a distribution. We use techniques from
Time-frequency Analysis, such as the modulation and Wiener amalgam spaces, and
also results of microlocal regularity of linear partial differential operators.
