Lomb Periodogram
- Identifies periodic signals in time series by fitting sinusoids using least-squares.
- Designed to estimate the strength (power) of periodic components even when noise and non-periodic components are present.
- Commonly applied in fields such as astronomy, geophysics, and signal processing.
Definition
Section titled “Definition”The Lomb periodogram is a type of spectral estimation method used to identify significant periodic signals in a time series data set. It is based on the concept of least-squares fitting of sinusoidal functions to the data.
Explanation
Section titled “Explanation”The method fits sinusoidal functions to time series data using least-squares techniques to estimate the presence and strength (power) of periodic components. It employs approaches such as windowing and detrending alongside the least-squares fits to help isolate periodic signals from noise and other non-periodic components in the data. Because of these steps, the Lomb periodogram can accurately detect and estimate periodic signals even when noise and non-periodic behavior are present.
Examples
Section titled “Examples”Example 1: Astronomy
Section titled “Example 1: Astronomy”In astronomy, the Lomb periodogram is often used to search for periodic signals in the light curves of stars. A light curve is a plot of the brightness of a star over time and can reveal information about the star’s behavior, such as its rotation rate or the presence of any orbiting planets. By applying the Lomb periodogram to the light curve data, astronomers can identify periodic signals and use them to make inferences about the star.
Example 2: Geophysics
Section titled “Example 2: Geophysics”In geophysics, the Lomb periodogram can be used to study periodic signals present in geophysical data such as earthquakes, tides, or ocean currents. By applying the method to this type of data, geophysicists can identify and analyze periodic signals and use them to gain insight into the underlying processes that generate the signals. For example, periodic signals in earthquake data can provide clues about the structure and behavior of the earth’s crust, while periodic signals in ocean current data can reveal information about circulation patterns of the oceans.
Use cases
Section titled “Use cases”- Astronomy: searching for periodic signals in stellar light curves to infer rotation rates or orbiting bodies.
- Geophysics: analyzing periodic components in earthquakes, tides, and ocean currents.
- Signal processing: identifying and estimating periodic signals within noisy time series data.
Related terms
Section titled “Related terms”- Spectral estimation
- Least-squares fitting
- Sinusoidal functions
- Windowing
- Detrending
- Time series
- Power (of periodic signals)