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. The significance of the peak in Figure b would indicate, falsely, that there is a secondary frequency. In order to distinguish real secondaries from artifacts of the filtering process, the data is filtered on either side of the primary frequency. The filtered data sets are then reanalyzed for the secondary frequency. If the secondary frequency shows a dependence with respect to the filtering frequency, then the signal is an artifact of the filtering process and cannot be considered real.