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.
['Huixia He', 'David J. Thomson']
The Canonical Bicoherence—Part II: QPC Test and Its Application in Geomagnetic Data