The Canonical Bicoherence—Part II: QPC Test and Its Application in Geomagnetic Data

Author

He, HuiXia ; Thomson, David J.

Author_Institution

Dept. of Phys. & Astron., Univ. of Western Ontario, London, ON

Volume

57

Issue

4

fYear

2009

fDate

4/1/2009 12:00:00 AM

Firstpage

1285

Lastpage

1292

Abstract

In a companion paper [ldquoThe canonical bicoherence-Part I: Definition, multitaper estimation, and statistics,rdquo IEEE transactions on signal processing, vol. 57, no. 4, April 2009], we defined the canonical bicoherence (CBC), proposed its multitaper estimates, showed its feasibility to detect quadratic phase coupling (QPC) for multivariate random processes, and discussed its statistical properties. In this part, the canonical biphase (CBP) is defined, and a two-step QPC test is developed using the first canonical bicoherence and the first canonical biphase at prescribed significance levels. Detection probabilities of this test are given by Monte Carlo simulations. The canonical bicoherence is applied to analyze the possibility of quadratic phase couplings in the Earth´s magnetic field. The results of simulations show that lower-frequency p -modes of the Sun may interact nonlinearly, producing intermodulation components at the sum and/or difference of fundamental frequency modes of oscillations.

Keywords

Monte Carlo methods; geomagnetism; geophysical signal processing; intermodulation; random processes; Earth magnetic field; Monte Carlo simulations; QPC test; Sun; canonical bicoherence; canonical biphase; fundamental frequency modes; geomagnetic data; intermodulation components; lower-frequency p-modes; multivariate random processes; quadratic phase coupling detect; statistical properties; Canonical bicoherence (CBC); QPC test; canonical biphase (CBP); geomagnetic field; solar $p$-mode;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2009.2012603

Filename

4749277