AN IDENTIFICATION OF THE FREQUENCIES AND AMPLITUDES OF THE TRIGONOMETRIC SERIES

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