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The linear scale invariant systems are introduced for both integer and fractional orders. They are defined by the generalized Euler-Cauchy differential equation. The quantum fractional derivatives are suitable for dealing with this kind of systems, allowing us to define impulse response and transfer function with the help of the Mellin transform. It is shown how to compute the impulse responses corresponding to the two half plane regions of convergence of the transfer function.

A look into fractional calculus and its applications from the signal processing point of view is done in this paper. A coherent approach to the fractional derivative is presented, leading to notions that are not only compatible with the classic but also constitute a true generalization. This means that the classic are recovered when the fractional domain is left. This happens in particular with the impulse response and transfer function. An interesting feature of the systems is the causality that the fractional derivative imposes. The main properties of the derivatives and their representations are presented. A brief and general study of the fractional linear systems is done, by showing how to compute the impulse, step and frequency responses, how to test the stability and how to insert the initial conditions. The practical realization problem is focussed and it is shown how to perform the input?ouput computations. Some biomedical applications are described.

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.

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