Course content:

• Time Series Analysis: Methods for evenly sampled data
• Time Series Analysis: Methods for unevenly sampled data
• Timing methods in Optical and X-ray Astronomy
• Timing features in Optical and X-ray Astronomy

Theoretical and practical considerations will be supplemented with the home exercises which constitute the important part of the course.

Literature:

• Fourier Analysis of Time Series: An Introduction (2nd edition – 2000) – P. Bloomfield: ISBN: 978-0-471-88948-9
• Asteroseismology (2010) – C. Aerts, J. Christensen-Dalsgaard, D. W. Kurtz: ISBN: 978-1-4020-5178-4
• Fourier techniques in X-ray timing (1988) – M. van der Klis: can be downloaded from here
• Fourier Analysis with Unequally-Spaced Data (1975) – T. J. Deeming: can be downloaded from here
• Astronomical Time Series Analysis: Lecture Notes – Jaan Pelt: can be downloaded from here

Schedule:

• Lecture 1: January 7: Introduction (Time Series, Light Curves, Time, Phase, Ephemeris)
  PDF
• Lecture 2: January 10: Introduction (Simplest methods of Time Series Analysis, Frequency).
  PDF * Light Curve (to download click right mouse button and “Save Link As”)
• Lecture 3: January 16: Harmonic Analysis. Fourier transform. Continuous and Discrete Fourier transforms, Power Density Spectrum.
  PDF
• Exercise session: January 21: How Continuous and Discrete FT are connected? Discrete FT of a sinusoid.
  Program set N1 * Viewer (simple plotting utilites) * Light Curve (sin)
• Lecture 4 and Exercise session: January 23: How Continuous and Discrete FT are connected? Discrete FT of a sinusoid.
  PDF

• Exercise session: January 28: Power Density Spectrum. Poisson noise.
  Poisson data * Light Curves (eclipses and skewed-sin)
• Lecture 5: January 31: Leahy normallization. Statistics of Power Spectra. Useful tips.
  PDF
• Exercise session: February 4: Statistics of Power Spectra.
  TimeRebin * Conf. level data * QPO 1
• Exercise session at home: February 6.
  Data for practical work * TimeRebin
• Lecture 6: February 11: Spectral Analysis with Unevenly-Spaced Data. Discrete Fourier Transform. Lomb-Scargle periodogram. Combined analysis of power spectra. Dealing with Aliases. CLEAN algorithm.
  PDF * Paper (Deeming) * Paper (Sturrock) * Lomb-Scargle Win & Src * CLEAN
• Exercise session at home: February 13.
  Real Data for practice
• Lecture 7: February 18: Spectral Analysis with Unevenly-Spaced Data (cont.): Non-parametric Frequency Analysis Methods. Comparison of PDM and the LS method.
  PDF
• Lecture 8: February 20: Time Series Analysis in the Time Domain. Cross-Correlation. Autocorrelation. O-C Diagram. Detrending.
  PDF
• Lecture 9: February 26: Conclusion.
  PDF