  We present a theoretical study of high-order harmonic generation (HHG) driven
by ultrashort optical pulses with different kind of chirps. The goal of the
present work is perform a detailed study to clarify the relevant parameters in
the chirped pulses to achieve a noticeable cut-off extensions in HHG. These
chirped pulses are generated using both linear and nonlinear dispersive
media.The description of the origin of the physical mechanisms responsible of
this extension is, however, not usually reported with enough detail in the
literature. The study of the behaviour of the harmonic cut-off with these kind
of pulses is carried out in the classical context, by the integration of the
Newton-Lorentz equation complemented with the quantum approach, based on the
integration of the time dependent Schr\"odinger equation in full dimensions
(TDSE-3D), we are able to understand the underlying physics.
