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 $f(t)=a_0+ sumlimits_{j=1}^N[a_jcos{omega}_jt+b_j;sin{omega}_jt]$ 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.