GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS
OF CARDIOVASCULAR DATA
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BROAD-BAND SMOOTHING

Smoothing technique for power spectra  in which the resulting frequency resolution and estimation variance are not constant over the frequency axis, as in conventional spectra

Broad-band spectra quantify blood pressure and heart-rate variabilities over a very broad range of frequencies. In these applications the need to preserve high resolution at the lower frequencies may be incompatible with the opposite need to largely reduce the estimation variance at higher frequencies: thus, what may be considered an optimum trade-off between frequency resolution and estimation variance in a frequency band might be unacceptable at other frequencies. A particular smoothing scheme, called broad-band smoothing, allows to obtain frequency resolution and estimation variance which are not constant over the frequency axis, thus allowing to obtain different trade-off between resolution and variance at different frequencies. This smoothing procedure consists in averaging adjacent spectral lines, where the number of lines to average changes with the frequency, usually increasing with the log of the frequency.

 Left: unsmoothed FFT spectrum of blood pressure from a 8-h recording: this spectrum is characterized by a very high frequency resolution, but also by a very high estimation variance. Centre: the same spectrum smoothed by a moving average filter of order 250 (i.e., average over 250 adjacent spectral lines). Estimation variance is largely reduced, but the frequency resolution dramatically worsens and important spectral details may be lost at the lower frequencies. Right: broad-band spectrum obtained from the raw FFT spectrum by averaging adjacent spectral lines: in this case the number of lines to average increases with the frequency from 1 to 250. The desired reduction of the estimation variance is obtained at the highest frequencies preserving the original frequency resolution at the lowest frequencies.

References:
Castiglioni P et al (1999) Broad-band spectral analysis of 24-h continuous finger blood pressure: comparison with intra-arterial recordings. Clin. Sci..
Di Rienzo M et al (1996) Effects of sino-aortic denervation on spectral characteristics of blood pressure and pulse interval variability: a wide-band approach. Med Biol Eng Comput.

(PC 07-09-1999)

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