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.2011.26.4.603
Published online 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
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