AN IDENTIFICATION OF THE FREQUENCIES AND AMPLITUDES OF THE TRIGONOMETRIC SERIES

Title & Authors
AN IDENTIFICATION OF THE FREQUENCIES AND AMPLITUDES OF THE TRIGONOMETRIC SERIES
Chung, Ji-Chan; Kang, Min-Soo; Kim, Soo-Han; Ko, Il-Seog;

Abstract
In this paper, we propose an algorithm for identifying $\small{{\omega}_j{\in}(0,\;{\infty}),\;a_j,b_j{\in}\mathbb{C}}$ and N of the following trigonometric series $\small{f(t)=a_0+ \sum\limits_{j=1}^N[a_jcos{\omega}_jt+b_j\;sin{\omega}_jt]}$ 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.
Keywords
trigonometric series;Hankel determinant;signal processing;
Language
English
Cited by
References
1.
A. El Badia and T. Ha-Duong, An inverse source problem in potential analysis, Inverse Problems 16 (2000), no. 3, 651-663.

2.
A. El Badia, Inverse source problem in an anisotropic medium by boundary measure- ments, Inverse Problems 21 (2005), no. 5, 1487-1506.