Updated 08 Jan 2022
The least-squares wavelet analysis (LSWA) is a robust method of analyzing any type of time/data series without the need for editing and preprocessing of the original series. The LSWA can rigorously analyze any non-stationary and equally/unequally spaced series with an associated covariance matrix that may have trends and/or datum shifts. The least-squares cross-wavelet analysis complements the LSWA in the study of the coherency and phase differences of two series of any type. A MATLAB software package including a graphical user interface is developed for these methods to aid researchers in analyzing pairs of series. The package also includes the least-squares spectral analysis, the antileakage least-squares spectral analysis, and the least-squares cross-spectral analysis to further help researchers study the components of interest in a series. We demonstrate the steps that users need to take for a successful analysis using three examples: two synthetic time series, and a Global Positioning System time series.
Ebrahim Ghaderpour (2022). LSWAVE-SignalProcessing (https://github.com/Ghaderpour/LSWAVE-SignalProcessing), GitHub. Retrieved .
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “Least-Squares Wavelet Analysis of Unequally Spaced and Non-Stationary Time Series and Its Applications.” Mathematical Geosciences, vol. 49, no. 7, Springer Nature, June 2017, pp. 819–44, doi:10.1007/s11004-017-9691-0.
Ghaderpour, Ebrahim, et al. “Antileakage Least-Squares Spectral Analysis for Seismic Data Regularization and Random Noise Attenuation.” GEOPHYSICS, vol. 83, no. 3, Society of Exploration Geophysicists, Mar. 2018, pp. V157–V170, doi:10.1190/geo2017-0284.1.
Ghaderpour, Ebrahim, et al. “Least-Squares Cross-Wavelet Analysis and Its Applications in Geophysical Time Series.” Journal of Geodesy, vol. 92, no. 10, Springer Nature, May 2018, pp. 1223–36, doi:10.1007/s00190-018-1156-9.
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “LSWAVE: a MATLAB Software for the Least-Squares Wavelet and Cross-Wavelet Analyses.” GPS Solutions, vol. 23, no. 2, Springer Nature, Mar. 2019, doi:10.1007/s10291-019-0841-3.
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