Two-component bivariate signal decomposition based on time-frequency analysis

A time-frequency analysis based approach for the decomposition of bivariate signals is presented. In particular, the well-known problem of two components overlapping in the time-frequency plane while having non-linear instantaneous frequencies is considered. The bivariate form of data leads to a significant modification of the Wigner distribution cross-terms. Therefore, the eigenvalue decomposition of Wigner distribution based signal autocorrelation matrix produces two significant eigenvalues instead of one in the common Wigner distribution. It is shown that the two corresponding eigenvectors can be linearly combined in order to produce fully separated signal components. The unknown coefficients are found by minimizing the time-frequency concentration measure of these particular eigenvectors linear combination. The presented approach is illustrated on the decomposition of a fast-varying real-valued signal with small instantaneous frequencies, so that its positive and negative frequency parts are so close that they degrade the analytical signal representation.