Kendall's advanced theory of statistics
Kendall's advanced theory of statistics
Time series: data analysis and theory
Time series: data analysis and theory
Multitaper estimators of polyspectra
Signal Processing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The canonical bicoherence-part II: QPC test and its application in geomagnetic data
IEEE Transactions on Signal Processing
Canonical bicoherence analysis of dynamic EEG data
Journal of Computational Neuroscience
| Hi-index | 35.69 |
The central theme of this pair of papers (Parts I and II) [IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol. 57, no. 4, April 2009] is a new definition: the canonical bicoherence, a combination of the canonical coherence and the bicoherence. The canonical bicoherence is an effective tool for analyzing quadratic nonlinearity in multivariate signals. In this first part, the definition and properties of the canonical bicoherence are presented. The feasibility of the canonical bicoherence in detecting quadratic phase coupling (QPC) of mnltivariate signals is explained theoretically, illustrated by an example, and verified by numerical simulations. Multitaper methods and a sequence of three singular value decompositions (SVD's) are used to estimate canonical bicoherences, to achieve reliable estimates with a reasonable amount of memory and computation time. Finally, we show that the canonical bicoherence estimate has an approximate asymptotic κXv2-distribution, and the weighted jackknife method, used over tapers and segments, is applied to estimate variances of multitaper canonical bicoherence estimates.