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 An identification of the frequencies and amplitudes of the trigonometric series Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 603-610 https://doi.org/10.4134/CKMS.2011.26.4.603Printed December 1, 2011 Ji Chan Chung, Min Soo Kang, Soo Han Kim, and Il Seog Ko Gyeonggi Science High School, Hongchun High School, Yushin High School, Gyeonggi Science High School Abstract : In this paper, we propose an algorithm for identifying $\omega_j \in (0,\infty)$, $a_j, b_j \in \mathbb{C}$ and $N$ of the following trigonometric series $$f(t)= a_0 + \sum_{j=1}^N \big[ a_j \cos \omega_j t + b_j \sin \omega_j t \big]$$ by means of the finite number of sample values. We prove that the frequency components are shown to be the solutions of some characteristic equation related to the inverse of a Hankel matrix derived from the sample values. Keywords : trigonometric series, Hankel determinant, signal processing MSC numbers : Primary 42A15; Secondary 15B05 Downloads: Full-text PDF

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