Abstract: The method described in this report deals with the problems of T-wave detection in an ECG. Determining the position of a T-wave is complicated due to the low amplitude, the ambiguous and changing form of the complex. A wavelet transform approach handles these complications and therefore a method based on this concept was developed. A QRS-complex detection method was customised by revising the scales and adjusting and polishing the decision rules. This way we developed a detection method that is able to detect T-waves with a sensitivity of 93% and a correct-detection ratio of 93% even with a serious amount of baseline drift and noise.

Abstract: The surface profiles resulting from a laser beam melt ablation process have been quantified on the basis of the multifractal formalism. The multifractal spectra for several parameters sets, obtained with the wavelet transform modulus maxima method, were found to change towards higher Holder exponents as the system undergoes a regime transition from medium to high ablation rates. This is consistent with the experimental observation of pattern formation at high ablation rates.

Abstract: Objectives: Our objectives were to study the temporal correlation of physical activity time series in patients with chronic fatigue syndrome (CFS) during normal daily life and to examine if it could identify the altered physical activity in these patients. Methods: Fractal scaling exponents of diurnal and nocturnal physical activity time series in 10 CFS patients and 6 healthy control subjects (CON) were calculated by the detrended fluctuation analysis (DFA) and the wavelet transform modulus maxima (WTMM) method. We hypothesized that, due to their illness- and/or fatigue-induced resting episodes, altered physical activity patterns in CFS patients might be observed at the interruption of activity bursts. Thus, we further developed a new method, the wavelet transform negative modulus maxima (WTNMM) method, which could evaluate the temporal correlation at the interruption of activities. We compared the fractal scaling exponents for CFS and CON by each method. Results: Both for CFS and CON, we found the fractal time structures in their diurnal physical activity records for at least up to 35 minutes. No group difference was found in nocturnal activities. The WTNMM method revealed that, in diurnal activities, CFS patients had significantly (p <0.01) smaller fractal scaling exponent (0.87 ± 0.03) compared to controls (1.01 ± 0.03). Such a difference was identified neither by the DFA nor WTMM method. Conclusions: CFS patients had more abrupt interruptions of voluntary physical activity during diurnal periods in normal daily life, probed by the decreased correlation in the negative modulus maxima of the wavelet-transformed activity data, possibly due to their exaggerated fatigue.

Abstract: . Magnetospheric cusps are regions which are characterized by highly turbulent plasma. We have used Polar magnetic field data to study the structure of turbulence in the cusp region. The wavelet transform modulus maxima method (WTMM) has been applied to estimate the scaling exponent of the partition function and singularity spectra. Their features are similar to those found in the nonlinear multifractal systems. We have found that the scaling exponent does not allow one to conclude which intermittency model fits the experiment better. However, the singularity spectra reveal that different models can be ascribed to turbulence observed under various IMF conditions. For northward IMF conditions the turbulence is consistent with the multifractal p-model of fully developed fluid turbulence. For southward IMF experimental data agree with the model of non-fully developed Kolmogorov-like fluid turbulence.

Abstract: We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and monofractal 3D fractional Brownian vector fields. We report the results of some application to the velocity and vorticity fields issued from 3D isotropic turbulence simulations. This study reveals the existence of an intimate relationship between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.