  A qubit can be used as a sensitive spectrum analyzer of its environment. Here
we show how the problem of spectral analysis of noise induced by a strongly
coupled environment can be solved for discrete spectra. Our analytical model
shows non-linear signal dependence on noise power, as well as possible
frequency mixing, both are inherent to quantum evolution. This model enabled us
to use a single trapped ion as a sensitive probe for strong, non-Gaussian,
discrete magnetic field noise. To overcome ambiguities arising from the
non-linear character of strong noise, we develop a three step noise
characterization scheme: peak identification, magnitude identification and
fine-tuning. Finally, we compare experimentally equidistant versus Uhrig pulse
schemes for spectral analysis. The method is readily available to any quantum
probe which can be coherently manipulated.
