An alternative method for power spectral density (PSD) estimation—the Daniell method—is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion—the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

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The Nlog(N) scaling law and the increase in computation time for the Daniell method were tested in Matlab on an intel® Core™ i7 processor with averaging factor M up to 105. The computations times for the data in Figure 1 were performed on the same computer.

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