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In a recent paper [Int. J. Quant. Chem. (2016) DOI: 10.1002/qua.25144,arXiv:1502.06579] Markovich, Blau, Sanders, and Aspuru-Guzik presented anumerical evaluation and comparison of three methods, Compressed Sensing (CS),Super-Resolution (SR), and Filter Diagonalization (FDM), on their ability of"recovering information" from time signals, concluding that CS and RSoutperform FDM. We argue that this comparison is invalid for the followingreasons. FDM is a well established method designed for solving the harmonicinversion problem or, similarly, for the problem of spectral estimation, and assuch should be applied only to problems of this kind. The authors incorrectlyassume that the problem of data fitting is equivalent to the spectralestimation problem, regardless of what parametric form is used, and,consequently, in all five numerical examples FDM is applied to the wrongproblem. Moreover, the authors' implementation of FDM turned out to beincorrect, leading to extremely bad results, caused by numerical instabilities.As we demonstrate here, if implemented correctly, FDM could still be used forfitting the data, at least for the time signals composed of damped sinusoids,resulting in superior performance. In addition, we show that the publishedarticle is full of inaccuracies, mistakes and incorrect statements.

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