  Here, we explore the prospects of carrying out the single qubit spectroscopy
of environmental noise when the resolution of the frequency filters produced by
the dynamical decoupling pulse sequences can be set high enough to reveal the
discrete structure of the noise spectral density. The standard form of
spectroscopy is applicable when the filter is unable to resolve the discrete
spectral lines and only coarse grained approximation of the spectrum is
recorded in the qubit's decoherence rate. When the discrete structure becomes
accessible, the qubit probe evolves in a qualitatively different manner, and
the procedure for recovering spectral density has to be redesigned.
