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
