We study global wave front sets given by matrices of Wigner type and defined in spaces of globally \(\omega \) -tempered ultradistributions of Beurling type, extending and completing the results in Asensio (J Pseudo-Differ Oper Appl 14(2):27, 2023). In fact, this approach permits to unify previous analyses in the literature of this field and to include other quadratic time-frequency analysis representations that had not been considered there. Moreover, we prove that the range of matrices is optimal, in the sense that no further matrix-Wigner transform could describe the spaces of globally \(\omega \) -rapidly decreasing functions in terms of seminorms. Finally, wave front sets for concrete distributions are calculated.
