  We consider the $1$- and $2$-d bicomplex analogs of the classical
Fourier--Wigner transform. Their basic properties, including Moyal's identity
and characterization of their ranges giving rise to new bicomplex--polyanalytic
functional spaces are discussed. Particular case of special window is also
considered. An orthogonal basis for the space of bicomplex--valued square
integrable functions on the bicomplex numbers is constructed by means of the
polyanalytic complex Hermite functions.
