This paper proposes a combined coarse-grained multifractal method to discriminate between distressed and normal foetuses. The coarse-graining operation was performed by means of a coarse-grained procedure and the multifractal operation was based on a structure function. The proposed method was evaluated by one hundred recordings including eighty normal foetuses and twenty distressed foetuses. We found that it was possible to discriminate between distressed and normal foetuses using the Hurst exponent, singularity, and Holder spectra. 1. Introduction Foetal distress is often the result of reduction in respiratory exchange between the mother and the foetus. In most cases, foetal distress is strongly related to intrauterine growth retardation [1]. Early identification of distressed status from heart rate variability is highly important since it can help the obstetrician to decide on immediate delivery by caesarean section. The value of analysis of heart rate variability (HRV) to provide a means of diagnosis and prognosis of heart disease is now well established. HRV time series has now become the elementary basis from which most analyses and processes are operated. Due to the nonstationary and nonlinear nature of HRV time series, many recent studies have tried to take full advantage of the nonlinear nature of heart rate variability by analysing the complexity of time series. This complexity analysis of the foetal heart rate (FHR) that has its roots in adult HRV research can be conceived of in many ways. However, it was probably the scale invariance properties observed through power law spectral density [2] that was the triggering element for several studies based on the multiscale analysis of HRV [3, 4]. Among the overall complexity descriptors, entropy descriptors [3, 5, 6] with fractal dimension estimators [7–10] were probably the first “nonconventional” tools used to study FHR. Certain studies even used multifractal features of FHR. The research studies by Ivanov et al. were probably the first to demonstrate multifractality in cardiac dynamics as well as in physiologic dynamics in general [11–13]. These seminal studies were then followed by researches such as [14–17], to name but a few. The starting point of the present study was based on two approaches, the first being that of Wang et al. [15] focusing on the multifractal analysis of adult ECG signals with a coarse-graining approach initially proposed by [18]. The second approach was based on the studies by [19, 20] and more recently those of [16, 21, 22] that themselves used a method based on a
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