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At this point, the combined spectrum of all the equivalent layers should approximately match the spectrum of the data (Fig. 11d).
Let us assume S 1, S 2, …, S M are the FTIR spectra under consideration and S μ is the average spectrum of the data set.
The cut-off wavelengths, and information about the contribution of the short and long wavelengths in the spectrum, can be obtained from the calculated radially-averaged power spectrum of the data.
The dominant frequency of the interior noise at 75.0 Hz was confirmed from the spectrum of the data and the modal analysis results, and originated from the peak vibration of the top slab due to resonance and the first-order vertical acoustic mode, which led to cavity resonance, amplifying the corresponding noise.
In addition to the investigation of the oxygen green line emission rates, this study also shows that HHT is a powerful spectral analysis tool which presents the time-frequency-energy spectrum of the data with very high temporal and spectral resolutions.
Reanalysis of the power spectrum of the data using alternate methods based on the Lomb-Scargle [11] [13] transform, which does not require evenly spaced data and therefore no rebinning, is a robust test of whether binning and interpolation introduced any artifacts.
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The method involves construction of a "Data Ensemble" consisting of three distinct spectra: Data spectrum: The data spectrum is calculated from conventional Fourier processing of the acquired FID.
Thus, Equation (9) establishes the existing relationship, ∀l, between the circular cross-spectra of the data and the sources.
The circular spectra of the data and the sources are defined as follows: S X C l = 1 N l ∑ ω ∈ Z l X C ω X C ω ∗ (6).
We used the spectral angle mapper (SAM) algorithm to cluster the spectra of the data set according to their similarity to endmember spectra (Fig. 1b, c).
A pressed BaSO4 powder was used as a reference, and the absorption spectra of the data were transformed from the diffuse reflection spectra according to the Kubelka-Munk (K-M) theory.
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