Least Squares Spectral Analysis (LSSA)
Synopsis of the theory
Find a summary of the theory in this link.
LSSA has several advantages over the commonly known Fourier transform, such as:
- Time series with unequally spaced values can be analyzed without pre-processing
- Time series does not have to be continuous (allowance of data gaps)
- Time series with an associated covariance matrix can be analyzed
- Time series can have datum shifts and trends
- No limitations for the length of the time series
- Higher accuracy achieved with longer time series
- Statistical testing on the significance of spectral peaks can be performed
Main characteristics of the software
The Least Squares Spectral Analysis software was first developed by Vaníček (1968, 1971) as an alternative to the classical Fourier methods. It has been revised by Wells, Vaníček and Pagiatakis in 1985 in order to eliminate certain bugs and to be more versatile. The most recent version (v.5.02) had a number of modifications implemented by Pagiatakis (1998).
In its most fundamental level, the LSSA software allows the user to specify the so-called known constituents, which can be datum bias, linear trend, forced periodic constituents or "anything else" defined by the user.
The only subroutines changed are those which specify the input: TSPEC, TIMSER and DRIVER.
In subroutine TSPEC one has to take care in redimensioning the parameters FF(NF) and T(NF), which represent the vector of time series values and their corresponding time tags vector, respectively, where NF is the number of measurements. In addition, redimensioning of the parameter PER is necessary if forced periodic constituents are to be eliminated.
In subroutine DRIVER one has to specify the period for each spectral value through PL and PS, and also, the number of frequencies to be computed in this period, by NW.
In subroutine TIMSER one has to redimension the parametersF(NF) and T(NF) as done in subroutine TSPEC. If there are forced periodic constituents to be eliminated, the redimensioning of PCNPERD and PERCNPERD is needed, where NPER represents the number of forced periods. In this case, the vector P of (forced) periods for which spectral values will be computed has to be defined.
Besides, the known constituents have to be defined accordingly. For example, NDAT = 1 (if there is no datum bias); LT = 1 (if there is a linear trend); and, NPER depending on the number of forced periods.
The software presents as output the time series, the spectrum, a solution for the known constituents, such as amplitude and phase, and the correlations between them.
Please, refer to the Manual add link for details on using LSSA v.5.02.