Preprint Article Version 1 This version is not peer-reviewed

A simple Spectral Observer

Version 1 : Received: 3 March 2018 / Approved: 5 March 2018 / Online: 5 March 2018 (06:57:35 CET)
Version 2 : Received: 25 April 2018 / Approved: 26 April 2018 / Online: 26 April 2018 (07:53:32 CEST)

A peer-reviewed article of this Preprint also exists.

Torres, L.; Jiménez-Cabas, J.; Gómez-Aguilar, J.F.; Pérez-Alcazar, P. A Simple Spectral Observer. Math. Comput. Appl. 2018, 23, 23. Torres, L.; Jiménez-Cabas, J.; Gómez-Aguilar, J.F.; Pérez-Alcazar, P. A Simple Spectral Observer. Math. Comput. Appl. 2018, 23, 23.

Journal reference: Math. Comput. Appl. 2018, 23, 23
DOI: 10.3390/mca23020023

Abstract

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. This paper proposes a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients and (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08.

Subject Areas

Signal processing; Fourier series; state observer

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