Spectral estimates of heart rate variability (HRV) often involve the use of techniques such as the fast Fourier transform (FFT), which require an evenly sampled time series. HRV is calculated from the variations in the beat-to-beat (RR) interval timing of the cardiac cycle which are inherently irregularly spaced in time. In order to produce an evenly sampled time series prior to FFT-based spectral estimation, linear or cubic spline resampling is usually employed. In this paper, by using a realistic artificial RR interval generator, interpolation and resampling is shown to result in consistent over-estimations of the power spectral density (PSD) compared with the theoretical solution. The Lomb-Scargle (LS) periodogram, a more appropriate spectral estimation technique for unevenly sampled time series that uses only the original data, is shown to provide a superior PSD estimate. Ectopy removal or replacement is shown to be essential regardless of the spectral estimation technique. Resampling and phantom beat replacement is shown to decrease the accuracy of PSD estimation, even at low levels of ectopy or artefact. A linear relationship between the frequency of ectopy/artefact and the error (mean and variance) of the PSD estimate is demonstrated. Comparisons of PSD estimation techniques performed on real RR interval data during minimally active segments (sleep) demonstrate that the LS periodogram provides a less noisy spectral estimate of HRV.