Communications of the
Korean Mathematical Society CKMS

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