  Context: Several approaches to estimate frequency, phase and amplitude errors
in time series analyses were reported in the literature, but they are either
time consuming to compute, grossly overestimating the error, or are based on
empirically determined criteria. Aims: A simple, but realistic estimate of the
frequency uncertainty in time series analyses. Methods: Synthetic data sets
with mono- and multi-periodic harmonic signals and with randomly distributed
amplitude, frequency and phase were generated and white noise added. We tried
to recover the input parameters with classical Fourier techniques and
investigated the error as a function of the relative level of noise, signal and
frequency difference. Results: We present simple formulas for the upper limit
of the amplitude, frequency and phase uncertainties in time-series analyses. We
also demonstrate the possibility to detect frequencies which are separated by
less than the classical frequency resolution and that the realistic frequency
error is at least 4 times smaller than the classical frequency resolution.
