New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties.

In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.

Non-commensurate fractional linear systems: New results.

A study of non-commensurate fractional linear system is done in a parallel way to the commensurate case. A partial fraction decomposition is accomplished using a recursive procedure. Each partial fraction is inverted in two different ways. The decomposition integer/fractional is done also. Some examples are presented.

A multichannel time-frequency and multi-wavelet toolbox for uterine electromyography processing and visualisation.

The uterine electromyogram, also called electrohysterogram (EHG), is an electrical signal generated by the uterine contractile activity. The EHG has been considered a promising biomarker for labour and preterm labour prediction, for which there is a demand for accurate estimation methods. Preterm labour is a significant public health concern and one of the major causes of neonatal mortality and morbidity [1]. Given the non-stationary properties of the EHG signal, time-frequency domain analysis can be used. For real life signals it is not generally possible to determine a priori the suitable quadratic time-frequency kernel or the appropriate wavelet family and relative parameters, regarding, for instance, the adequate detection of the signal frequency variation in time. There has been a lack of a comprehensive software tool for the selection of the appropriate time frequency representation of a multichannel EHG signal and extraction of relevant spectral and temporal information. The presented toolbox (Uterine Explorer) has been specifically designed for the EHG analysis and exploration in view of the characterisation of its components. The starting point is the multichannel scalogram or spectrogram representation from which frequency and time marginals, instantaneous frequency and bandwidth are obtained as EHG features. From this point the detected components undergo parametric and non-parametric spectral estimation and wavelet packet analysis. Intrauterine pressure estimation (IUP) is obtained using the Teager, RMS, wavelet marginal and Hilbert operators over the EHG. This toolbox has been tested to build up a dictionary of 288 EHG components [2], useful for research in preterm labour prediction.