Power spectral density estimation is a commonly-used analytic technique for describing periodicities in time series. Most non-trivial analyses of heart rate variability (HRV) depend on PSD estimation. The instantaneous heart rate time series used as the bases of these analyses are sampled at intrinsically irregular intervals (if the RR intervals were uniform, there would be no HRV to analyze). Standard methods for PSD estimation, including Fourier transform (FT) and autoregressive (AR) methods, operate on time series with uniform intervals between samples. To apply FT or AR techniques to heart rate time series therefore requires that the series be resampled at uniform intervals[1, 2, 3]. The resampling process alters the frequency content of even a noise-free time series by nonlinear low-pass filtering (Figure 1).
If the time series contains inappropriate or missing samples (as, for example, in heart rate time series with ectopic beats or noise), PSD estimates can be severely affected, since impulse noise in the time domain is transformed to broad-band ``clutter'' in the frequency domain. In such cases, resampling is further complicated by the need to infer probable values as replacements, with the likelihood of further alteration of frequency content. For these reasons, some investigators analyze only segments free of ectopy and noise; this approach runs the risk of introducing selection bias in HRV analysis, however, since both ectopy and noise are correlated with HRV-related factors such as physical activity.
Methods for PSD estimation based directly on irregularly sampled time series have been used, though not in HRV analysis, since at least 1976[7, 8]. Methods such as the Lomb periodogram entirely avoid the problems associated with resampling and sample replacement. The high computational burden of these methods has been a major obstacle to their general use until recently. In 1989, Press and Rybicki published a fast algorithm for obtaining an arbitrarily accurate approximation to the Lomb periodogram[10, 11]. The remainder of this paper illustrates how the Lomb periodogram, obtained using the Press-Rybicki algorithm, may be applied to analysis of HRV and related signals.