  This paper introduces a couple of new time-frequency transforms, designed to
adapt their scale to specific features of the analyzed function. Such an
adaptation is implemented via so-called focus functions, which control the
window scale as a function of the time variable, or the frequency variable. In
this respect, these transforms are non-linear, which makes the analysis more
complex than usual.Under appropriate assumptions, some norm control can be
obtained for both transforms in L^2(R) spaces, which extend the classical
continuous frame norm control and guarantees well-definedness on L^2. Given the
non-linearity of the transforms, the existence of inverse transforms is not
guaranteed anymore, and is an open question. However, the results of this paper
represent a first step towards a more general theory.Besides mathematical
results, some elementary examples of time and frequency focus functions are
provided, which can serve as staring point for concrete applications.
