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A Poster about the Old History of Fractional Calculus

Tenreiro Machado, J.Kiryakova, VirginiaMainardi, Francesco — 2010

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

A new zoom algorithm and its use in frequency estimation

Manuel D. OrtigueiraAntónio S. SerralheiroJ. A. Tenreiro Machado — 2015

Waves, Wavelets and Fractals

This 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...

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