Detection and estimation using the third moment matrix

The third moment matrix R₃ is proposed as a tool for use in the detection and estimation of phase-coupled sine waves. The advantages of such an approach are that the structure of R₃ can be exploited by means of the singular value decomposition (SVD) to estimate directly the number of coupled sine waves and their frequencies. After a brief introduction to the bispectrum and the phase coupling problem, the following key results are presented: (1) The rank of R₃ is (asymptotically) equal to the number of coupled sine waves. (2) A pseudobispectrum can be generated using a MUSIC-like algorithm with vectors orthogonal to the (column) signal subspace. (3) The coupled frequencies can be directly estimated from the (row) signal subspace using techniques such as Root-MUSIC or ESPRIT. Examples of simulations using this approach are given