GLOSSARY OF
TERMS
USED
IN
TIME SERIES
ANALYSIS
OF CARDIOVASCULAR
DATA
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WIGNER-VILLE
DISTRIBUTION
Time-frequency
distribution of a signal with very high time and frequency resolution
The Wigner-Ville distribution of a signal s(t), W(t,f),
is defined as:
A valuable property of the Wigner-Ville distribution is that it satisfies
the marginal conditions. For a time-series
x(n), the expression of the discrete-time Wigner-Ville distribution,
WD(n,f) is:
where hN(k) is a data-window,
which performs a frequency smoothing. While Fourier spectra are periodic
with period equal to the sampling rate, WD(n,f) is periodic in frequency
with period equal to half the sampling rate. This may cause aliasing,
which can be removed either by oversampling, or by using the corresponding
analytic
signal.The distribution is negatively affected by important cross-terms,
which limit its practical use. Cross-terms may be adequately reduced smoothing
the distribution over time. The resulting smoothed Wigner-Ville, SWD(n,f)
is:
The time-resolution depends on the time-window
gM(m),
and it is lower in SWD than in WD. Moreover, SWD does not satisfy the marginal
conditions. To reduce the cross-terms satisfying the marginal conditions,
a larger class of time-frequency distributions, the Choi-Williams
distribution, which includes the Wigner-Ville as a special case, has
been proposed.
A Cross-Wigner Distribution has been also proposed for the time-variant
bivariate spectral analysis of nonstationary cardiovascular signals.
References
Novak
P., Novak V. (1993) Time/frequency mapping of the heart rate, blood
pressure and respiratory signals Med.&.Biol. eng. & Comput.
Novak
V et al (1993) Influence of respiration on heart rate and blood pressure
fluctuations.J Appl Physiol
Pola
S et. al (1996) Estimation of the power spectral density in nonstationary
cardiovascular time series: assessing the role of the time-frequency representations
(TFR). IEEE Trans Biomed Eng.
Pola S, et al Bivariate Spectral Analysis of Nonstationary
Cardiovascular Variability Series through Cross Wigner Distribution
Computers in Cardiology 1996, 81-84
Pola S et al (1995) Assessing Variability in Cardiovascular
Series during Autonomic Tests. in Computers analysis of Cardiovascular
Signals, M Di Rienzo (Ed.), IOS Press, 53-66.
Chan
HL et al (2001) Time-Frequency analysis of heart rate variability during
transient segments. Ann Biomed Eng.
(PC 25-02-2000)
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