@InProceedings{7362521,
  author = {K. Barbé and L. Lauwers and L. G. Fuentes},
  booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)},
  title = {Taylor-fourier series analysis for fractional order systems},
  year = {2015},
  pages = {938-942},
  abstract = {Dynamical systems describing a physical process with a dominant diffusion phenomenon require a large dimensional model due to their long memory. Without prior knowledge, it is however not straightforward to know if/whether one deals with a fractional order system or long memory effects. Since the parametric modeling of a fractional system is very involved, we tackle the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that the classical Fourier basis leading to the Frequency Response Function (FRF) lacks fractional insight. Therefore, we introduce a TaylorFourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: the Taylor-Fourier spectrum.},
  keywords = {Fourier series;frequency response;nonparametric statistics;spectral analysis;Taylor-Fourier series analysis;fractional order systems;dynamical systems;physical process;dominant diffusion phenomenon;large dimensional model;long memory effects;parametric modeling;classical Fourier basis;frequency response function;nonparametric insight;spectral content;Decision support systems;Europe;Signal processing;Conferences;Poles and zeros;Time-frequency analysis;Non-parametric modeling;dynamic systems;fractional order systems;Taylor-Fourier basis;theory of frames},
  doi = {10.1109/EUSIPCO.2015.7362521},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102515.pdf},
}

{"_id":"hnduAMP2FFFL62w7Y","bibbaseid":"barb-lauwers-fuentes-taylorfourierseriesanalysisforfractionalordersystems-2015","authorIDs":[],"author_short":["Barbé, K.","Lauwers, L.","Fuentes, L. G."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"firstnames":["K."],"propositions":[],"lastnames":["Barbé"],"suffixes":[]},{"firstnames":["L."],"propositions":[],"lastnames":["Lauwers"],"suffixes":[]},{"firstnames":["L.","G."],"propositions":[],"lastnames":["Fuentes"],"suffixes":[]}],"booktitle":"2015 23rd European Signal Processing Conference (EUSIPCO)","title":"Taylor-fourier series analysis for fractional order systems","year":"2015","pages":"938-942","abstract":"Dynamical systems describing a physical process with a dominant diffusion phenomenon require a large dimensional model due to their long memory. Without prior knowledge, it is however not straightforward to know if/whether one deals with a fractional order system or long memory effects. Since the parametric modeling of a fractional system is very involved, we tackle the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that the classical Fourier basis leading to the Frequency Response Function (FRF) lacks fractional insight. Therefore, we introduce a TaylorFourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: the Taylor-Fourier spectrum.","keywords":"Fourier series;frequency response;nonparametric statistics;spectral analysis;Taylor-Fourier series analysis;fractional order systems;dynamical systems;physical process;dominant diffusion phenomenon;large dimensional model;long memory effects;parametric modeling;classical Fourier basis;frequency response function;nonparametric insight;spectral content;Decision support systems;Europe;Signal processing;Conferences;Poles and zeros;Time-frequency analysis;Non-parametric modeling;dynamic systems;fractional order systems;Taylor-Fourier basis;theory of frames","doi":"10.1109/EUSIPCO.2015.7362521","issn":"2076-1465","month":"Aug","url":"https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102515.pdf","bibtex":"@InProceedings{7362521,\n author = {K. Barbé and L. Lauwers and L. G. Fuentes},\n booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)},\n title = {Taylor-fourier series analysis for fractional order systems},\n year = {2015},\n pages = {938-942},\n abstract = {Dynamical systems describing a physical process with a dominant diffusion phenomenon require a large dimensional model due to their long memory. Without prior knowledge, it is however not straightforward to know if/whether one deals with a fractional order system or long memory effects. Since the parametric modeling of a fractional system is very involved, we tackle the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that the classical Fourier basis leading to the Frequency Response Function (FRF) lacks fractional insight. Therefore, we introduce a TaylorFourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: the Taylor-Fourier spectrum.},\n keywords = {Fourier series;frequency response;nonparametric statistics;spectral analysis;Taylor-Fourier series analysis;fractional order systems;dynamical systems;physical process;dominant diffusion phenomenon;large dimensional model;long memory effects;parametric modeling;classical Fourier basis;frequency response function;nonparametric insight;spectral content;Decision support systems;Europe;Signal processing;Conferences;Poles and zeros;Time-frequency analysis;Non-parametric modeling;dynamic systems;fractional order systems;Taylor-Fourier basis;theory of frames},\n doi = {10.1109/EUSIPCO.2015.7362521},\n issn = {2076-1465},\n month = {Aug},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102515.pdf},\n}\n\n","author_short":["Barbé, K.","Lauwers, L.","Fuentes, L. G."],"key":"7362521","id":"7362521","bibbaseid":"barb-lauwers-fuentes-taylorfourierseriesanalysisforfractionalordersystems-2015","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102515.pdf"},"keyword":["Fourier series;frequency response;nonparametric statistics;spectral analysis;Taylor-Fourier series analysis;fractional order systems;dynamical systems;physical process;dominant diffusion phenomenon;large dimensional model;long memory effects;parametric modeling;classical Fourier basis;frequency response function;nonparametric insight;spectral content;Decision support systems;Europe;Signal processing;Conferences;Poles and zeros;Time-frequency analysis;Non-parametric modeling;dynamic systems;fractional order systems;Taylor-Fourier basis;theory of frames"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2015url.bib","creationDate":"2021-02-13T17:31:52.375Z","downloads":0,"keywords":["fourier series;frequency response;nonparametric statistics;spectral analysis;taylor-fourier series analysis;fractional order systems;dynamical systems;physical process;dominant diffusion phenomenon;large dimensional model;long memory effects;parametric modeling;classical fourier basis;frequency response function;nonparametric insight;spectral content;decision support systems;europe;signal processing;conferences;poles and zeros;time-frequency analysis;non-parametric modeling;dynamic systems;fractional order systems;taylor-fourier basis;theory of frames"],"search_terms":["taylor","fourier","series","analysis","fractional","order","systems","barbé","lauwers","fuentes"],"title":"Taylor-fourier series analysis for fractional order systems","year":2015,"dataSources":["eov4vbT6mnAiTpKji","knrZsDjSNHWtA9WNT"]}