Applications
The most useful feature of the LSSA method is enabling incomplete records to be spectrally analyzed, without the need to manipulate the record or to invent otherwise non-existent data.
Magnitudes in the LSSA spectrum depict the contribution of a frequency or period to the variance of the time series. Generally, spectral magnitudes defined in the above manner enable the output's straightforward significance level regime. Alternatively, magnitudes in the Vanícek spectrum can also be expressed in dB. Note that magnitudes in the Vaníček spectrum follow β-distribution.
Inverse transformation of Vaníček's LSSA is possible, as is most easily seen by writing the forward transform as a matrix; the matrix inverse (when the matrix is not singular) or pseudo-inverse will then be an inverse transformation; the inverse will exactly match the original data if the chosen sinusoids are mutually independent at the sample points and their number is equal to the number of data points. No such inverse procedure is known for the periodogram method.
Read more about this topic: Least-squares Spectral Analysis