Alternative Method to Estimate the Fourier Expansions and Its Rate of Change
This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the Kalman filter, consequently, the signal’s and su...
| Autores principales: | , , |
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| Formato: | Artículo |
| Lenguaje: | inglés |
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Molecular Diversity Preservation International
2022
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| Materias: | |
| Acceso en línea: | http://eprints.uanl.mx/29019/1/961.pdf |
| _version_ | 1824421123049127936 |
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| author | Rodríguez Maldonado, Johnny Posadas Castillo, Cornelio Zambrano Serrano, Ernesto |
| author_facet | Rodríguez Maldonado, Johnny Posadas Castillo, Cornelio Zambrano Serrano, Ernesto |
| author_sort | Rodríguez Maldonado, Johnny |
| collection | Repositorio Institucional |
| description | This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the Kalman filter, consequently, the signal’s and successive derivatives’ coefficients are obtained with the state prediction and the state matrix inverse. Compared to discrete Fourier transform (DFT), the new class of filters provides noise reduction and sidelobe suppression advantages. Additionally, the proposed Taylor–Kalman–Fourier algorithm (TKFA) achieves a null-flat frequency response around the frequency operation. Moreover, with the proposed TKFA method, the decrement in the inter-harmonic amplitude is more significant than that obtained with the Kalman–Fourier algorithm (KFA), and the neighborhood of the null-flat frequency is expanded. Finally, the approximation of the input signal and its derivative can be performed with a sumoffunctions related to the estimated coefficients and their respective harmonics. |
| format | Article |
| id | eprints-29019 |
| institution | UANL |
| language | English |
| publishDate | 2022 |
| publisher | Molecular Diversity Preservation International |
| record_format | eprints |
| spelling | eprints-290192025-01-23T14:42:33Z http://eprints.uanl.mx/29019/ Alternative Method to Estimate the Fourier Expansions and Its Rate of Change Rodríguez Maldonado, Johnny Posadas Castillo, Cornelio Zambrano Serrano, Ernesto QA Matemáticas, Ciencias computacionales This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the Kalman filter, consequently, the signal’s and successive derivatives’ coefficients are obtained with the state prediction and the state matrix inverse. Compared to discrete Fourier transform (DFT), the new class of filters provides noise reduction and sidelobe suppression advantages. Additionally, the proposed Taylor–Kalman–Fourier algorithm (TKFA) achieves a null-flat frequency response around the frequency operation. Moreover, with the proposed TKFA method, the decrement in the inter-harmonic amplitude is more significant than that obtained with the Kalman–Fourier algorithm (KFA), and the neighborhood of the null-flat frequency is expanded. Finally, the approximation of the input signal and its derivative can be performed with a sumoffunctions related to the estimated coefficients and their respective harmonics. Molecular Diversity Preservation International 2022 Article PeerReviewed text en cc_by_nc_nd http://eprints.uanl.mx/29019/1/961.pdf http://eprints.uanl.mx/29019/1.haspreviewThumbnailVersion/961.pdf Rodríguez Maldonado, Johnny y Posadas Castillo, Cornelio y Zambrano Serrano, Ernesto (2022) Alternative Method to Estimate the Fourier Expansions and Its Rate of Change. Mathematics, 10 (20). pp. 1-12. ISSN 2227-7390 http://doi.org/10.3390/math10203832 doi:10.3390/math10203832 |
| spellingShingle | QA Matemáticas, Ciencias computacionales Rodríguez Maldonado, Johnny Posadas Castillo, Cornelio Zambrano Serrano, Ernesto Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| thumbnail | https://rediab.uanl.mx/themes/sandal5/images/online.png |
| title | Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| title_full | Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| title_fullStr | Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| title_full_unstemmed | Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| title_short | Alternative Method to Estimate the Fourier Expansions and Its Rate of Change |
| title_sort | alternative method to estimate the fourier expansions and its rate of change |
| topic | QA Matemáticas, Ciencias computacionales |
| url | http://eprints.uanl.mx/29019/1/961.pdf |
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