Windowed-Wigner Representations, Interferences and Operators

``Windowed-Wigner'' representations, denoted by $\Wig_\psi$ and $\Wig_\psi^*$, were introduced in \cite{BogCarOli2012} in connection with uncertainty principles and interferences problems. In this paper we present a more precise analysis of their behavior obtaining an estimate of the $L^2$-norm of interferences of couples of ``model'' signals. We further define a suitable functional framework for the associated operators and show that they form a class of pseudo-differential operators which define a natural ``path'' between the multiplication, Weyl and Fourier multipliers operators.