Two results concerning chirps and 2-microlocal exponents prescription
Harmonic analysis on the Heisenberg nilpotent Lie group is not only concerned with quantum physics but also with information transmission channels [\textit{W. Schempp}, ``Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory'' (1986; Zbl 0632.43001)]. Due to the action of the metaplectic group, it allows to define chirp signals. In a more general parametrized setting, chirp signals can be used to provide information about the oscillatory behaviour of real-valued functions near a Hölder singularity that goes beyond the Hölder exponent characterization. The paper under review describes by means of two microlocalization techniques the local behaviour of such a function on the real line \(\mathbb{R}\). The parametrized description of the local behaviour is performed in terms of a combination of Hölder exponents as a measure of pointwise regularity and chirp exponents.
scientific article; zbMATH DE number 1228533