In order to solve the blind source separation (BSS) problems

a fast joint diagonalization (FJD) algorithm based on the diagonalization of a set of output auto-correlation matrices at different delays is proposed.The algorithm adopts a multiplicative update scheme to minimize the Frobenius-norm formulation of the approximate joint diagonalization problem.The special approximation of the cost function and the skilful denotation of concerning variables contribute to the highly computational efficiency of the algorithm.In each of multiplicative iterations

a strictly diagonally-dominant updated matrix is obtained

ensuring the invertibility of the diagonalizer and preventing the convergence to trivial values.The algorithm discards pre-whitening procedure

relaxes the positive-definiteness assumption on target matrices and can be used in complex-valued space

thus has more general utilizations.Computational complexity analysis shows the efficiency and easy implementation of FJD.Extensive numerical simulations illustrate the high convergent speed and good performance of FJD.Thus it can be used to solve the BSS problems efficiently.