Fourier techniques in X-ray timing

Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum and the signal variance, including corrections for binning and dead time. The statistical properties of a noise power spectrum are discussed and related to the problems of detection (and setting upper limits) of broad and narrow features in the power spectrum. A "dependent trial" method is discussed to search power spectra consistently for many different types of signal simultaneously. Methods are compared to detect a sinusoidal signal, a case that is relevant in the context of X-ray pulsars.