Harmonic timing analysis using periodograms

The search for harmonic signals in the presence of noise is a fundamental problem of timing analysis. This package provides a collection of periodogram implementations to approach this problem.

The cornerstone of this package is the implementation of the “Generalized Lomb-Scargle (GLS) periodogram”. The class is also available as a stand-alone module via the page of Mathias Zechmeister.

• The Generalized Lomb-Scargle Periodogram (GLS)
  • Example: Simple periodogram with default options
  • Example: Adding an error column and FAP levels
  • Example: Getting highest-power (best-fit) sine curve
  • API documentation

Classical Lomb-Scargle and FFT

PyAstronomy provides a class to calculate the Fast Fourier transform (Fourier). and a class to calculate the classical Lomb-Scargle periodogram (LombScargle). The latter can be treated as a special case of the GLS and the GLS class can be used to obtain it.

• Base classes
  • The TimeSeries base class
  • The PeriodBase Base class
• Classical Lomb-Scargle and FFT
  • The Fourier Transform
  • The Lomb-Scargle-Periodogram (fast)
• Examples
  • Fourier spectrum of evenly-sampled Poisson data
  • Error-weighted (generalized) Lomb periodogram

References

vdK

van der Klis, Fourier Techniques In X-Ray Timing

Leahy83

Leahy et al. 1983, “On searches for pulsed emission with application to four globular cluster X-ray sources - NGC 1851, 6441, 6624, and 6712”, 1983ApJ…266..160L

ZK09

Zechmeister & Kuerster 2009, “The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms”, 2009A&A…496..577Z

HB86

Horne & Baliunas 1986, “A prescription for period analysis of unevenly sampled time series”, 1986ApJ…302..757H

Scargle82

Scargle 1982, “Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data”, 1982ApJ…263..835S

NR

Numerical Recipes in C, Second edition