Spectral analysis of less-than-perfect stratigraphic time series is challenging for most spectral analysis techniques and requires some disconcerting relaxation of mathematical rigor which may compromise results. The Lomb-Scargle Fourier transform, as provided by SPECTRUM, is used to address this issue with controlled data sets, to demonstrate that interpretable results can be achieved in spite of such relaxation. Degraded complex synthetic frequency arrays which produce noisy spectra in time series analysis constrain the interpretation of spectra of natural time series. We use synthetic time series, degraded in different ways, to produce spectra which mimic those derived from the middle to late Viséan Windsor Group. With input frequencies describing predicted orbital parameters for the Viséan, the synthetic data set is a fundamental tool in validating strong orbital control over eustatic sea level change during the Asbian and Brigantian stages in Atlantic Canada. With the degraded synthetic data set we demonstrate that suggestive temporal variation within a time series can reflect variations in the ability of overlapping data subsets to record a known signal, rather than paleoclimatically important change in forcing function. We recommend the use of synthetic data sets as an interpretative aid in the search for orbital forcing in stratigraphic time series, particularly in older rock sequences.