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

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.

[1]  Rekha Jain,et al.  Discrete High-Frequency p-Modes , 1996 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  Carol G. Maclennan,et al.  Propagation of solar oscillations through the interplanetary medium , 1995, Nature.

[4]  William J. Chaplin,et al.  Skew-symmetric solar p modes in low-l BiSON data , 1999 .

[5]  S. Elgar,et al.  Statistics Of Incoherence And Biphase , 1989, Workshop on Higher-Order Spectral Analysis.

[6]  Louis J. Lanzerotti,et al.  Solar Modal Structure of the Engineering Environment , 2007, Proceedings of the IEEE.

[7]  Alan D. Chave,et al.  Bounded influence magnetotelluric response function estimation , 2004 .

[8]  A. Jiménez,et al.  An Estimation of the Acoustic Cutoff Frequency of the Sun Based on the Properties of the Low-Degree Pseudomodes , 2006 .

[9]  Steve McLaughlin,et al.  Robust nonparametric bicoherence estimation by stepwise outlier rejection , 2000 .

[10]  Justin Fackrell,et al.  Bispectral analysis of speech signals , 1997 .

[11]  David J. Thomson,et al.  The Canonical Bicoherence—Part I: Definition, Multitaper Estimation, and Statistics , 2009, IEEE Transactions on Signal Processing.

[12]  P. L. Pallé,et al.  Frequencies, linewidths, and splittings of low-degree solar p-modes , 1990 .

[13]  Steve McLaughlin,et al.  Comparison of quadratic phase coupling detectors on sonar data , 2003, Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492).

[14]  S. Elgar,et al.  Statistics of bicoherence and biphase , 1989 .

[15]  David J. Thomson,et al.  Baseline and distribution estimates of complicated spectra , 2000, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496).

[16]  Gabrielle Berthomieu,et al.  Low-frequency p- and g-mode solar oscillations , 2000 .