Article
Version 1
Preserved in Portico This version is not peer-reviewed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)
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.
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.
Keywords
Signal processing; Fourier series; state observer
Subject
Engineering, Control and Systems Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
