A Simple Spectral Observer
Por:
Torres, Lizeth, Jimenez-Cabas, Javier, Francisco Gomez-Aguilar, Jose, Perez-Alcazar, Pablo
Publicada:
1 jun 2018
Resumen:
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. A spectral observer can be
catalogued as an online algorithm for time-frequency analysis because is
a method that can compute on the fly the Fourier Transform (FT) of a
signal, without having the entire signal available from the start. In
this regard, this paper presents 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, (4) the fitting
of the historical Bitcoin market data from 1 December 2014 to 8 January
2018 and (5) the estimation of a input force acting upon a Duffing
oscillator. To round out this paper, we present a detailed discussion
about the results of the applications as well as a comparative analysis
of the proposed spectral observer vis-a-vis the Short Time Fourier
Transform (STFT), which is a well-known method for time-frequency
analysis.
Filiaciones:
Torres, Lizeth:
Univ Nacl Autonoma Mexico, Inst Ingn, Catedras CONACYT, Ciudad De Mexico 04510, Mexico
Jimenez-Cabas, Javier:
Univ Costa, Dept Ciencias Informat & Elect, Barranquilla, Colombia
Francisco Gomez-Aguilar, Jose:
Tecnol Nacl Mexico, Catedras CONACYT, Ctr Nacl Invest & Desarrollo Tecnol, Cuernavaca 62490, Morelos, Mexico
Perez-Alcazar, Pablo:
Univ Nacl Autonoma Mexico, Fac Ingn, Ciudad De Mexico 04510, Mexico
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