Atomic functions (AF) and Kravchenko-Rvachev’s window functions based on them are proposed to be applied for the Choi-Williams analysis of the ultrawideband (UWB) signals. New class of the non-linear Choi-Williams-Rvachev transforms (ChWRT) is considered. The advantages and disadvantages of such transforms are discussed. The abilities of the ChWRT at the sample of the UWB signal model analysis are demonstrated.