Abstract
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more important in high-energy astronomy. Many sophisticated tools are available for data analysis, and complex practical aspects are described in technical papers. Here, we present the basic concepts upon which all these techniques are based. It is intended as a condensed primer of Fourier analysis, dealing with fundamental aspects that can be examined in detail elsewhere. It is not intended to be a presentation of detailed Fourier tools for data analysis, but the reader will find the theoretical basis to understand available analysis techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P.S. Addison, The Illustrated Wavelet Transform Handbook (IoP, Bristol/Philadelphia, 2002)
T. Belloni, G. Hasinger, An atlas of aperiodic variability in HMXB. A&A 230, 103–119 (1990)
T. Belloni, M. van der Klis, W.H.G. Lewin et al., Energy dependence in the quasi-periodic oscillations and noise of black hole candidates in the very high state. A&A 322, 857–867 (1997)
T. Belloni, D. Psaltis, M. van der Klis, A unified description of the timing features of accreting X-ray binaries. ApJ 572, 392–406 (2002)
T. Butz, Fourier Transformation for Pedestrians (Springer, Berlin/Heidelberg, 2006)
L. Cohen, Time-Frequency Analysis (Prentice-Hall, Upper Saddle River, 1995)
J.W. Cooley, J.W. Tukey, An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
L. Eyer, P. Bartholdi, Variable stars: which Nyquist frequency? A&AS 135, 1–3 (1999)
G.M. Jenkins, D.G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968)
D.A. Leahy, W. Darbro, R.F. Elsner et al., On searches for pulsed emission with application to four globular cluster X-ray sources: NGC 1851, 6441, 6624, and 6712. ApJ 266, 160–170 (1983)
N.R. Lomb, Least-squares frequency analysis of unequally spaced data. Ap&SS 39, 447–462 (1976)
S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. (Academic Press, San Diego, 2009)
M. Nowak, Are there three peaks in the power spectra of GX 339-4 and Cyg X-1? MNRAS 318, 361 (2000)
D.B. Percival, A.T. Walden, Wavelet Methods for Time Series Analysis (Cambridge University Press, Cambridge, 2000)
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes – The Art of Scientific Computing, 3rd edn. (Cambridge University Press, Cambridge, 2007)
J.D. Scargle, Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. ApJ 263, 835–853 (1982)
M. van der Klis, Fourier techniques in X-ray timing, in Timing Neutron Stars, ed. by H. Ogelman, E.P.J. van den Heuvel. NATO ASI Series C, Vol. 262 (Kluwer, Dordrecht, 1988) pp. 27–70
J.T. VanderPlas, Understanding the Lomb-Scargle Periodogram. ApJS 236, 16 (2018)
H.J. Weaver, Theory of Discrete and Continuous Fourier Analysis (Wiley, New York, 1989)
Acknowledgements
The authors thank S. Motta for useful comments. T.M.B. acknowledges financial contribution from PRIN INAF 2019 n.15.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2022 Springer Nature Singapore Pte Ltd.
About this entry
Cite this entry
Belloni, T.M., Bhattacharya, D. (2022). Basics of Fourier Analysis for High-Energy Astronomy. In: Bambi, C., Santangelo, A. (eds) Handbook of X-ray and Gamma-ray Astrophysics. Springer, Singapore. https://doi.org/10.1007/978-981-16-4544-0_136-1
Download citation
DOI: https://doi.org/10.1007/978-981-16-4544-0_136-1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-4544-0
Online ISBN: 978-981-16-4544-0
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics