Time-Frequency Analysis for Nonstationary Time Series

We examined whether the nonlinear control mechanism of the fetal autonomic nervous system would change in various fetal states. Eight thousand or more fetal heartbeats were detected from normal, hypoxemic, and acidemic fetuses. Fetal heart Doppler-signal intervals were determined in a high-precision autocorrelation method, and a time series of fetal heart rate fluctuation was obtained. The distribution of the amplitude of temporal fluctuation in the low-frequency component of fetal heart rate frequency was studied using a method of time-frequency analysis called wavelet transform. Spline 4 was used as the mother wavelet function. A gamma distribution was observed from 17 wk of gestation onward. The value of the parameter ν of this gamma distribution was ∼1.6 and remained constant regardless of the gestational age or the time of day. The value of ν decreased significantly to 0.77 when the fetus developed acidemia and was 1.51 in hypoxemia and 1.54 in a normal condition. This study elucidates a nonlinear structure of the time series of heart rate fluctuation of the gamma distribution in the human fetus. This technique may provide a new quantitative index of fetal monitoring to diagnose fetal acidemia.

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Adaptive window selection and smoothing of lomb periodogram for time-frequency analysis of time series

The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04. ◽

10.1109/mwscas.2004.1354110 ◽

2004 ◽

Cited By ~ 1

Author(s):

Shing-Chow Chan ◽

Zhiguo Zhang

Keyword(s):

Time Series ◽

Frequency Analysis ◽

Time Frequency Analysis ◽

Time Frequency ◽

Adaptive Window ◽

Window Selection ◽

Analysis Of Time Series

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A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

Nonlinear Processes in Geophysics ◽

10.5194/npg-25-175-2018 ◽

2018 ◽

Vol 25 (1) ◽

pp. 175-200 ◽

Cited By ~ 2

Author(s):

Guillaume Lenoir ◽

Michel Crucifix

Keyword(s):

Time Series ◽

Wavelet Transform ◽

Frequency Analysis ◽

Continuous Wavelet Transform ◽

Background Noise ◽

Noise Model ◽

Analysis Tool ◽

Continuous Wavelet ◽

Time Frequency Analysis ◽

Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighbouring times in order to reduce its variance. The Shannon–Nyquist exclusion zone is however defined as the area corrupted by local aliasing issues. The local amplitude in the time–frequency plane is then estimated with least-squares methods. We also derive an approximate formula linking the squared amplitude and the scalogram. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

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