Ortigueira, MD, Rodríguez-Germá L, Trujillo JJ.
2011.
Complex Grünwald?Letnikov, Liouville, Riemann?Liouville, and Caputo derivatives for analytic functions Communications in Nonlinear Science and Numerical Simulation.
AbstractThe well-known Liouville, Riemann?Liouville and Caputo derivatives are extended to the complex functions space, in a natural way, and it is established interesting connections between them and the Grünwald?Letnikov derivative. Particularly, starting from a complex formulation of the Grünwald?Letnikov derivative we establishes a bridge with existing integral formulations and obtained regularised integrals for Liouville, Riemann?Liouville, and Caputo derivatives. Moreover, it is shown that we can combine the procedures followed in the computation of Riemann?Liouville and Caputo derivatives with the Grünwald?Letnikov to obtain a new way of computing them. The theory we present here will surely open a new way into the fractional derivatives computation.
Cardoso, E, Batista A, Rodrigues R, Ortigueira M, Bárbara C, Martinho C, Rato R.
2010.
A Contribution for the Automatic Sleep Classification Based on the Itakura-Saito Spectral Distance. Emerging Trends in Technological Innovation. 314:374–381.
AbstractSleep staging is a crucial step before the scoring the sleep apnoea, in subjects that are tested for this condition. These patients undergo a whole night polysomnography recording that includes EEG, EOG, ECG, EMG and respiratory signals. Sleep staging refers to the quantification of its depth. Despite the commercial sleep software being able to stage the sleep, there is a general lack of confidence amongst health practitioners of these machine results. Generally the sleep scoring is done over the visual inspection of the overnight patient EEG recording, which takes the attention of an expert medical practitioner over a couple of hours. This contributes to a waiting list of two years for patients of the Portuguese Health Service. In this work we have used a spectral comparison method called Itakura distance to be able to make a distinction between sleepy and awake epochs in a night EEG recording, therefore automatically doing the staging. We have used the data from 20 patients of Hospital Pulido Valente, which had been previously visually expert scored. Our technique results were promising, in a way that Itakura distance can, by itself, distinguish with a good degree of certainty the N2, N3 and awake states. Pre-processing stages for artefact reduction and baseline removal using Wavelets were applied.
] 