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Comments on ‘‘Modeling fractional stochastic systems as non-random fractional d...
Ortigueira, M.D.Applied Mathematical Modelling, Vol.33 ; Some results presented in the paper ‘‘Modeling fractional stochastic systems as nonrandom fractional dynamics driven Brownian motions” [I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999] are discussed in this paper. The slightly modified Grünwald-Letnikov derivative proposed there is used to deduce some interesting results that are in contr...
An introduction to the fractional continuous- time linear systems: the 21st cen...
Ortigueira, M.D.IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter ; A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We wi...
Fractional central differences and derivatives
Ortigueira, M.D.Journal of Vibration and Control, Vol. 14, Nº 9-10 ; Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier tran...
On the HHT, its problems, and some solutions
Ortigueira, M.D.; Rato, R.T.; Batista, A. G.Mechanical Systems and Signal Processing, Vol.22, Number 6 ; The empirical mode decomposition (EMD) is reviewed and some questions related to its effective performance are discussed. Its interpretation in terms of AM/FM modulation is done. Solutions for its drawbacks are proposed. Numerical simulations are carried out to empirically evaluate the proposed modified EMD.
On the relation between the fractional Brownian motion and the fractional deriv...
Ortigueira, M.D.; Batista, A. G.Physics Letters A, vol. 372; Issue 7 ; The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for thes...
An introduction to the fractional continuous-time linear systems
Ortigueira, M.D.A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fracti...
On the fractional central differences and derivatives
Ortigueira, M.D.Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivati...
New quasi-orthogonal BCH-derived sequences for CDMA applications
Ortigueira, M.D.; Ricardo, Cesaltina N. E.; Gerald, José António B.European Transactions on Telecommunications, vol. 18 ; Based on two methods recently proposed—the ‘Ranging Criterion’ (RC) and the ‘Generators Ranging Criterion’ (GRC)—new (quasi orthogonal) even BCH-derived sequences are generated which are very attractive for synchronous or quasi-synchronous Code Division Multiple-Access (CDMA) systems. Numerical results show that the new family of BCH-derived sequences can ...
Pseudo-fractional ARMA modelling using a double Levinson recursion
Ortigueira, M.D.; Serralheiro, António J.IET Control Theory & Applications, Vol. 1, Nº 1 ; The modelling of fractional linear systems through ARMA models is addressed. To perform this study, a new recursive algorithm for impulse response ARMA modelling is presented. This is a general algorithm that allows the recursive construction of ARMA models from the impulse response sequence. This algorithm does not need an exact order specification, as it give...
Potential dementia biomarkers based on the time-varying microstructure of sleep...
Ortigueira, M.D.; Ktonas, P. Y.; Golemati, S.; Xanthopoulos, P.Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007 ; The time-varying microstructure of sleep EEG spindles may have clinical significance in dementia studies. In this work, the sleep spindle is modeled as an AM-FM signal and parameterized in terms of six parameters, three quantifying the instantaneous envelope (IE) and three quantifying...
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