TY - JOUR
T1 - A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples
AU - Gómez, Gerard
AU - Mondelo, Josep Maria
AU - Simó, Carles
PY - 2010/7/1
Y1 - 2010/7/1
N2 - The purpose of this paper is to develop a numerical procedure for the determination of frequencies and amplitudes of a quasi-periodic function, starting from equally-spaced samples of it on a finite time interval. It is based on a collocation method in frequency domain. Strategies for the choice of the collocation harmonics are discussed, in order to ensure good conditioning of the resulting system of equations. The accuracy and robustness of the procedure is checked with several examples. The paper is ended with two applications of its use as a dynamical indicator. The theoretical support for the method presented here is given in a companion paper [21].
AB - The purpose of this paper is to develop a numerical procedure for the determination of frequencies and amplitudes of a quasi-periodic function, starting from equally-spaced samples of it on a finite time interval. It is based on a collocation method in frequency domain. Strategies for the choice of the collocation harmonics are discussed, in order to ensure good conditioning of the resulting system of equations. The accuracy and robustness of the procedure is checked with several examples. The paper is ended with two applications of its use as a dynamical indicator. The theoretical support for the method presented here is given in a companion paper [21].
KW - Collocation method
KW - Fast fourier transform
KW - Numerical fourier analysis
KW - Quasi-periodic functions
UR - https://www.scopus.com/pages/publications/77957816363
U2 - 10.3934/dcdsb.2010.14.41
DO - 10.3934/dcdsb.2010.14.41
M3 - Article
SN - 1531-3492
VL - 14
SP - 41
EP - 74
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 1
ER -