Data driven sampling of oscillating signals

The reduction of the number of samples is a key issue in signal processing for mobile applications. We investigate the link between the smoothness properties of a signal and the number of samples that can be obtained through a level crossing sampling procedure. The algorithm is analyzed and an upper bound of the number of samples is obtained in the worst case. The theoretical results are illustrated with applications to fractional Brownian motions and the Weierstrass function

Incompressible Stars and Fractional Derivatives

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum mechanics. In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions or stress conditions. To better understand the fractional effects, we discuss effective values for the density, gravitational field and equation of state. The fractional ob- jects are smaller and less massive than integer models. The fractional parameters are related to a polytropic index for the models considered

Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs

Considerations about the choice of a differintegrator

Proceedings of the 2nd International Conference on Computational Cybernetics, Vienna University of Technology, August 30 - September 1, 2004Despite 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 difierintegration definition problem from a systems point of view. Both local (GrunwaldLetnikov) and global (convolutional) 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 .

A Robust Variable Step Size Fractional Least Mean Square (RVSS-FLMS) Algorithm

In this paper, we propose an adaptive framework for the variable step size of the fractional least mean square (FLMS) algorithm. The proposed algorithm named the robust variable step size-FLMS (RVSS-FLMS), dynamically updates the step size of the FLMS to achieve high convergence rate with low steady state error. For the evaluation purpose, the problem of system identification is considered. The experiments clearly show that the proposed approach achieves better convergence rate compared to the FLMS and adaptive step-size modified FLMS (AMFLMS).Comment: 15 pages, 3 figures, 13th IEEE Colloquium on Signal Processing & its Applications (CSPA 2017

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal equations that allow us to obtain the ARMA parameters. This new LS is then applied to the same examples as in [R.S. Barbosa, J.A. Tenreiro Machado, I.M. Ferreira, Least-squares design of digital fractional-order operators, FDA’2004 First IFAC Workshop on Fractional Differentiation and Its Applications, Bordeaux, France, July 19–21, 2004, P. Ostalczyk, Fundamental properties of the fractional-order discrete-time integrator, Signal Processing 83 (2003) 2367–2376] so performance comparisons can be drawn. Simulation results show that both magnitude frequency responses are essentially identical. Concerning the modeling stability, both algorithms present similar limitations, although for different ARMA model orders

Fractional-order signal processing using a polymer-electrolyte transistor

Journal ArticleFractional-order systems have applications in the areas of Flight Control, Robotics, Missile Guidance, Control of Structural Vibrations of Space Platforms and Sensor Technology. Fractional-order transfer functions can characterize complex nonlinear dynamics with many fewer parameters than integer-order functions. This paper addresses the use of a polymer-electrolyte transistor (PET) for use in implementating fractional-order algorithms for signal processing. The PET's advantage over the conventional RC and RL circuits is that it can be both functionally scaled and varied for dynamic fractional-order parameter controllability