Percorrer por autor "Ortigueira, Manuel D."
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- Considerations about the choice of a differintegratorPublication . Ortigueira, Manuel D.; Machado, J. A. Tenreiro; Costa, J. Sá daDespite the great advances in the theory and applications of fractional calculus, some topics remain unclear making difficult its use in a systematic way. This paper studies the fractional differintegration definition problem from a systems point of view. Both local (Grunwald-Letnikov) and global (convoluntional) definitions are considered. It is shown that the Cauchy formulation must be adopted since it is coherent with usual practice in signal processing and control applications...
- Fractional signals and systems - editorialPublication . Ortigueira, Manuel D.; Machado, J. A.Tenreiro; Trujillo, Juan J.; Vinagre, Blas M.The word fractional acquired a new glamour at the beginning of the XXI century. Searching the web we count millions of references about this topic. In fact, we find it in a lot of apparently different scientific fields that in a first glance seem not to have any connection, but that verified to be a good strategy to adopt in their studies. Here we focus our attention into two of the most interesting and useful fractional areas: the Fractional Calculus and the Fractional Fourier transform.
- Integer/fractional decomposition of the impulse response of fractional linear systemsPublication . Ortigueira, Manuel D.; Machado, J. A. Tenreiro; Rivero, Margarita; Trujillo, Juan J.The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.
- New discrete-time fractional derivatives based on the bilinear transformation: Definitions and propertiesPublication . Ortigueira, Manuel D.; Machado, J. A. TenreiroIn 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.
- A new zoom algorithm and its use in frequency estimationPublication . Ortigueira, Manuel D.; Serralheiro, António S.; Machado, J. A. TenreiroThis paper presents a novel zoom transform algorithm for a more reliable frequency estimation. In fact, in many signal processing problems exact determination of the frequency of a signal is of paramount importance. Some techniques derived from the Fast Fourier Transform (FFT), just pad the signal with enough zeros in order to better sample its Discrete-Time Fourier Transform. The proposed algorithm is based on the FFT and avoids the problems observed in the standard heuristic approaches. The analytic formulation of the novel approach is presented and illustrated by means of simulations over short-time based signals. The presented examples demonstrate that the method gives rise to precise and deterministic results.
- Rhapsody in fractionalPublication . Machado, J. A. Tenreiro; Lopes, António M.; Duarte, Fernando B.; Ortigueira, Manuel D.; Rato, Raul T.This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.
- Riesz potential versus fractional LaplacianPublication . Ortigueira, Manuel D.; Laleg-Kirati, Taous-Meriem; Machado, J. A. TenreiroThis paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.
- Riesz potential versus fractional LaplacianPublication . Ortigueira, Manuel D.; Laleg-Kirati, Taous-Meriem; Machado, J. A. TenreiroThis paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.