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: September 7: Introduction (Time Series, Light Curves, Time)
  PDF
• Lecture 2: September 8: Introduction (Frequency, Phase, Ephemeris, Simplest methods of Time Series Analysis).
  PDF * Light Curve
• Lecture 3: September 10: Harmonic Analysis. Fourier transform.
  PDF
• Lecture 4: September 14: Continuous and Discrete Fourier transforms, Power Density Spectrum.
  PDF * Program set N1 * Light Curve (sin)
• Lecture 5 and Exercise session: September 15: Discrete FT of a sinusoid.
  PDF
• Lecture 6: September 17: Power Density Spectrum. Leahy normallization.
  PDF * Poisson data * Light Curve (eclipses)
• Lecture 7: September 21: Statistics of Power Spectra. Useful tips.
  PDF * Viewer * TimeRebin * Conf. level data * Simulated data
• Lecture 8 and Exercise session: September 22:
  Real Data 1
• Exercise session at home: September 23: Analysis of Real Data
• Lecture 9: September 28: Spectral Analysis with Unevenly-Spaced Data. Discrete Fourier Transform.
  PDF * Paper (Deeming) * Test Data
• Lecture 10: September 29: Spectral Analysis with Unevenly-Spaced Data. DFT (cont.).
  PDF (the same file)
• Lecture 11: October 1: Spectral Analysis with Unevenly-Spaced Data (cont.): Lomb-Scargle periodogram. Combined analysis of power spectra.
  PDF * Paper (Sturrock) * Lomb-Scargle Win * Lomb-Scargle Src
• Exercise session at home: October 5.
  Real Data 2
• Lecture 12: October 6: Spectral Analysis with Unevenly-Spaced Data (cont.): Dealing with Aliases. CLEAN algorithm. Non-parametric Frequency Analysis Methods. Comparison of PDM and the LS method.
  PDF
• Lecture 13: October 12: Time Series Analysis in the Time Domain. Cross-Correlation. Autocorrelation. O-C Diagram.
  PDF