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@ARTICLE{Pozza:906952,
      author       = {Pozza, Nicola Dalla and Gherardini, Stefano and Müller,
                      Matthias and Caruso, Filippo},
      title        = {{R}ole of the filter functions in noise spectroscopy},
      journal      = {International journal of quantum information},
      volume       = {17},
      number       = {08},
      issn         = {0219-7499},
      address      = {Singapore [u.a.]},
      publisher    = {World Scientific},
      reportid     = {FZJ-2022-01770},
      pages        = {1941008 -},
      year         = {2019},
      abstract     = {The success of quantum noise sensing methods depends on the
                      optimal interplay between properly designed control pulses
                      and statistically informative measurement data on a specific
                      quantum-probe observable. To enhance the information content
                      of the data and reduce as much as possible the number of
                      measurements on the probe, the filter orthogonalization
                      method has been recently introduced. The latter is able to
                      transform the control filter functions on an orthogonal
                      basis allowing for the optimal reconstruction of the noise
                      power spectral density. In this paper, we formalize this
                      method within the standard formalism of minimum mean squared
                      error estimation and we show the equivalence between the
                      solutions of the two approaches. Then, we introduce a
                      nonnegative least squares formulation that ensures the
                      nonnegativeness of the estimated noise spectral density.
                      Moreover, we also propose a novel protocol for the design in
                      the frequency domain of the set of filter functions. The
                      frequency-designed filter functions and the nonnegative
                      least squares reconstruction are numerically tested on noise
                      spectra with multiple components and as a function of the
                      estimation parameters.},
      cin          = {PGI-8},
      ddc          = {510},
      cid          = {I:(DE-Juel1)PGI-8-20190808},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / ASTERIQS - Advancing Science and TEchnology
                      thRough dIamond Quantum Sensing (820394)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(EU-Grant)820394},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000519696100007},
      doi          = {10.1142/S0219749919410089},
      url          = {https://juser.fz-juelich.de/record/906952},
}