Nonorthogonal joint diagonalization of spatial quadratic time-frequency matrices for source separation

The separation problem of an instantaneous mixture of deterministic or random source signals is addressed. We show that the separation can be realized through the nonorthogonal joint diagonalization of spatial quadratic time-frequency matrices. One advantage of the proposed method is that it does not require any whitening stage, and thus, it is intended to work even with a class of correlated signals. We also propose a general automatic time-frequency point selection procedure for the determination of the above matrices to be joint diagonalized. An analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones.