  We introduce an anisotropic global wave front set of Gelfand--Shilov
ultradistributions with different indices for regularity and decay at infinity.
The concept is defined by the lack of super-exponential decay along power type
curves in the phase space of the short-time Fourier transform. This wave front
set captures the phase space behaviour of oscillations of power monomial type,
a k a chirp signals. A microlocal result is proved with respect to
pseudodifferential operators with symbol classes that give rise to continuous
operators on Gelfand--Shilov spaces. We determine the wave front set of certain
series of derivatives of the Dirac delta, and exponential functions.
