Kovacs' derivation assumes a single signal with Gaussian noise and even data spacing, but Baliunas et al. For uniformly-spaced data, the fundamental and Nyquist frequencies specify the limits of the spectral window in which periodicity analysis may be performed. For unevenly-spaced data, the fundamental frequency is still well defined, but the Nyquist frequency is not. The pseudo-Nyquist frequency can then be determined by measuring the separation of the harmonic signals from the primary signal. For evenly-spaced data, there is no spectral information above the Nyquist limit.
Problems can arise however because of noise and under-sampling.
In some cases the nearest harmonic and primary signals will be negligibly different, so a clear determination based strictly on the photometric data cannot always be made. The finite Fourier transform has demonstrated itself as inadequate for the harmonic filtering of unevenly-spaced data sets. In these formulas, the parentheses mean inner products . Secondary peaks can result from the filtering process itself as well as true periodicity. Figure 2-3b shows the periodogram for same sine wave after the primary frequency has been removed from the signal.