  Understanding the physical origin of noise affecting quantum systems is
important for nearly every quantum application. Quantum noise spectroscopy has
been employed in various quantum systems, such as superconducting qubits, NV
centers and trapped ions. Traditional spectroscopy methods are usually
efficient in measuring noise spectra with mostly monotonically decaying
contributions. However, there are important scenarios in which the noise
spectrum is broadband and non-monotonous, thus posing a challenge to existing
noise spectroscopy schemes. Here, we compare several methods for noise
spectroscopy: spectral decomposition based on the Carr-Purcell-Meiboom-Gill
(CPMG) sequence, the recently presented DYnamic Sensitivity COntrol (DYSCO)
sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO). The
performance of the sequences is quantified by analytic and numeric
determination of the frequency resolution, bandwidth and sensitivity, revealing
a supremacy of gDYSCO to reconstruct non-trivial features. Utilizing an
ensemble of nitrogen-vacancy centers in diamond coupled to a high density
$^{13}$C nuclear spin environment, we experimentally confirm our findings. The
combination of the presented schemes offers potential to record high quality
noise spectra as a prerequisite to generate quantum systems unlimited by their
spin-bath environment.
