## Lomb-Scargle

The Lomb-Scargle method transforms an (unequally-spaced) time series into a power spectrum, using a technique known as the Lomb periodogram. The method was derived by Lomb1 in 1976, with improvements by Scargle2 in 1982. Although the Lomb-Scargle periodogram decomposes the data into a series of sine and cosine functions, it is similar to least-squares â€˜statisticalâ€™ methods (aiming at minimizing the difference between observed and modeled data). Peranso uses the algorithm defined by Scargle, but optimized using the Horne and Baliunas method3, which scales the periodogram by the total variance of the data, yielding a better estimation of the frequency of the periodic signal. It is a quite powerful method for finding weak periodic signals. The Lomb-Scargle dialog box exists in two forms: a simple form or an extended form (see pictures below). The only difference between both is that the extended form allows to select a different period analysis method. They contain following sections: - Base: Peranso by default calculates periods in days, which is typical for variable star work. Minor planet periods are usually expressed in hours. You can select which base to use in this section.
- Unit: this section allows to toggle between Time or Frequency domain based calculations. If you select Time, the X axis values will be expressed in days (or hours). If you select Frequency, the X axis values will be expressed in cycles per day (c/d) or cycles per hour (c/h).
- Range: enter Start and End values to define the period scan range. Resolution defines the step size to be used by Peranso in the period analysis. A high value will ensure that you won't miss any significant peak, but at the cost of CPU time. Step size = (End - Start) / Resolution.
Click Apply to start the period calculations. A progress bar pops up and remains visible till all calculations have completed. When done, a new Period Window appears. Close the Period determination dialog box by clicking the Cancel button.
Lomb-Scargle Period determination Extended (1) Lomb, N.R., 1976, Ap&SS, 39, 447 (2) Scargle, J.D., 1982, Ap.J., 263, 835 (3) Horne, J.H., Baliunas, S.L., 1986, ApJ, 302, 757 |