Averaging or Smoothing the periodogram. One major shortcoming with classical spectral analysis is that the fluctuations in the periodogram introduced by noise are roughly of the same magnitude as those caused by cyclic physiologic phenomena. More frequent sampling cannot eliminate this property. However Bartlett (23) suggested that, by averaging sequential periodograms, statistically superior behavior can be obtained, and this approach is now widely used; see Myers et al. and Bigger et al. for two typical applications to RR variability (24,25). Also, for spectral estimation of heart rate data, it is generally necessary only to know the power within a range of frequencies. If this range encompasses a sufficient number of discrete points at which the Fourier transform is computed, the power present In the band is also statistically well-behaved (20), making periodogram estimation of RR frequency domain information reasonable even on single windows. periodogram data is inherently "spiky," and, although this does not affect statistical validity, it is unattractive and sometimes difficult to appreciate visually. The periodogram can be "smoothed" to overcome these drawbacks without affecting its statistical properties or substantially increasing the time necessary for its computation. There are also other refinements and variations to classical spectral estimation that can improve the resolution or statistical properties of the resulting spectra (21).
Parametric Identification Techniques (Autoregression). Yule approached spectral analysis with an alternative method, in which a linear predictive model is fitted to the time-series data (26). As applied to the analysis of RR variability these techniques typically use regression techniques to predict an RR interval from a linear combination of the immediately prior RR intervals. The popularity of these parametric identification techniques has expanded concomitant with the development of efficient computational algorithms (27). They do not obsolete classical spectral analysis, but provide another approach in which a signal can typically be represented as a sum of a smaller number of periodic components chosen at specific frequencies at which power is maximal. For analysis of RR variability data the ability to obtain a small number of discrete frequencies has been the primary advantage of these techniques, rather than the high frequency resolution required for many applications in geophysics or communications. This simpler frequency decomposition facilitates cross-spectral analysis of RR interval data with other physiologic time series such as blood pressure (28). Because the spectrum is constructed from a mathematical function, it, is smooth and the high frequency peak resulting from respiratory (.vagal) modulation is clearly visible at the frequency of ventilation, about 0.25 Hz. The parametric identification process also identifies another peak at about 0.10 Hz with power exceeding that of the peak at 0.25 Hz. However, peaks centered at even lower frequencies that contain still greater energy may obscure the low frequency power. (Some investigators using parametric identification techniques subtract these lowest frequency peaks from the power spectral density to facilitate the display of peaks in the low frequency range).
Complex Demodulation. Another alternative for spectral analysis of RR interval data is complex demodulation (21). In this technique, a continuous estimate of power in the vicinity of a small number of discrete frequencies is produced. This approach is free from the theoretical requirement of stationarity, and the filter parameters can be adjusted to sufficiently separate the centers of the high and low frequency bands while maintaining a time resolution of less than one minute. Such an approach can be used, for example, to track the high frequency component representing vagal modulation of RR intervals in a variety of dynamic situations (29,30).
Prospects
Hypothesis Driven Signal Processing. The art of frequency domain analysis lies as much in extracting the biological information from the power spectrum as in producing a spectral estimate. An important example is in the use of frequency domain analysis to estimate sympathetic tone. It is known that increased sympathetic activity is reflected in increased low (0.04-0.15 Hz) frequency power (31). However, increases in vagal tone also result in increased power in the same low frequency band (32). Although different studies addressing this issue have used parametric or periodogram techniques, it is unlikely that this accounts for the different interpretations. In fact, the power spectral density estimates produced by these techniques are generally quite similar. However, parametric estimation techniques provide an estimate of power centered within a particular frequency band, independent of the tail distributions of other peaks that extend into the same region. "Low frequency power" defined as the energy contained in peaks centered in this band can differ substantially from "low frequency power" defined as the integrated spectral density in the frequency band; this is especially true because of an underlying l/f fluctuation (Figure 5) ubiquitously present in heart period signals (33). One definition or another might be most useful for addressing a specific physiological investigation; neither is mathematically "correct" or "incorrect." Because of this, it is especially important that the full details of spectral analysis are presented or available, because they are as integral to the final result as any other elements of the experimental design.
