Parameter estimation in epoch folding analysis

We describe a procedure that we have implemented to use epoch folding to estimate pulse period, shape, amplitude and phase (with uncertainties) for coherent oscillations in time series data. We improve on traditional techniques by fitting the as a function of test period with a response function which takes into account both data sampling and the oscillation pulse shape. It is shown that the epoch folding procedure makes optimum usage of the full pulse shape information, or equivalently all its Fourier components, in the period determination. An analytic expression for the period error is also given for this general, non-sinusoidal, case. The error estimate, which is equivalent to that for a least-squares fit of a set of harmonically related Fourier components, is verified by Monte Carlo simulations.