Multivariate Frequency and Amplitude Estimation for Unevenly Sampled Data Using and Extending the Lomb-Scargle...

Area of Science:

• Data Science
• Astronomy
• Signal Processing

Background:

• Conventional spectral analysis methods struggle with irregularly sampled data, causing significant biases.
• The classical Lomb-Scargle method (LSM) is effective for univariate, unevenly sampled time series.
• Extending LSM to multivariate data is crucial for analyzing complex, real-world datasets.

Purpose of the Study:

• To generalize the Lomb-Scargle method (LSM) for multivariate datasets with irregular sampling.
• To enable simultaneous estimation of frequency, phase, and amplitude vectors in complex data.
• To maintain the statistical robustness and noise resistance of the LSM.

Main Methods:

• Redefined the shifting parameter τ to preserve orthogonality of trigonometric basis functions in Rn.
• Applied the generalized LSM to randomly sampled 2D solar activity data (sunspots).
• Applied the generalized LSM to a 3D ultrasound velocity profile dataset with missing values and temporal jitter.

Main Results:

• Successfully identified characteristic frequencies in solar activity data.
• Achieved accurate velocity estimations in ultrasound measurements despite data imperfections.
• Demonstrated superior performance compared to Fourier Transform-based approaches through comparative analysis.

Conclusions:

• The generalized LSM offers a robust and statistically sound approach for frequency and amplitude estimation in multivariate, irregularly sampled data.
• This method significantly enhances the analysis of complex datasets in fields like solar physics and medical ultrasound.
• The derived confidence intervals and comparative analysis validate the method's effectiveness and reliability.