The Lomb-Scargle periodogram procedure was developed by astrophysicists who must often contend with data that are not evenly sampled. The utility of this algorithm is not limited strictly to unevenly spaced data, however. There are also benefits for uniformly sampled data.

This algorithm produces results nearly identical to an FFT, although it is not a traditional Fourier transform, and will not exactly reproduce FFT results. The algorithm essentially defines a second series of abscissa (time) values using a variable offset term in the definition of the PSD. This results in an algorithm that is equivalent to the least-squares fitting of sine curves (at specified frequencies) to the data.

This option is similar to the Fourier Spectrum option with an important exception that involves oversampling and spectral length selections. This spectral procedure also allows data with void values. These are simply removed from the data stream which then leads to unevenly sampled data.

Nyquist Issues

Data that have been unevenly sampled are not subject to an average Nyquist limitation. That is, spectral information at frequencies higher than the average Nyquist frequency is not automatically aliased to lower frequencies. The reason this is possible is that the uneven sampling trades off a complete information state within the Nyquist interval for an incomplete state, but one where some of the points are spaced much closer than the average sample interval. With unevenly sampled data, you can choose how far to "run out" the spectrum. The FlexPro implementation allows up to 4x the average Nyquist interval.

The spectrum length is not directly related to the length of the data stream. Further, the spectrum is computed only for real data (positive frequencies), does not include an initial zero frequency, and can be evaluated at any desired frequency set. Although FlexPro creates a uniformly spaced frequency spectrum similar to the FFT, this is not a requirement for the algorithm.

References

For more information, see:

•Jeffrey Scargle, Astrophysical Journal, v263, p.835 and William Press and G.B. Rybicki, Astrophysical Journal, v338, p.277.

See Also

Spectral Analysis Option

Uneven Data Fourier Spectral Analysis Object

FourierSpectrumUneven Function

Fourier Spectral Analysis

Fourier Spectral Analysis Tutorial