Journal of VLSI Signal Processing, ?, 1–13 (2001) c 2001 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Second Order Nonstationary Source Separation SEUNGJIN CHOI Department of Computer Science and Engineering, POSTECH, Korea ANDRZEJ CICHOCKI Lab for Advanced Brain Signal Processing, Brain Science Institute, RIKEN, Japan ADEL BELOUCHARNI Department of Electrical Engineering, Ecole Nationale Polytechnique, Algeria Received ?; Revised ? Editors: ? Abstract. This paper addresses a method of blind source separation that jointly exploits the nonstationarity and temporal structure of sources. The method needs only multiple time-delayed correlation matrices of the observation data, each of which is evaluated at different time-windowed data frame, to estimate the demixing matrix. The method is insensitive to the temporally white noise since it is based on only time-delayed correlation matrices (with non-zero time-lags) and is applicable to the case of either nonstationary sources or temporally correlated sources. We also discuss the extension of some existing methods with the overview of second-order blind source separation methods. Extensive numerical experiments confirm the validity and high performance of the proposed method. Keywords: Blind source separation, joint approximate diagonalization, noisy mixtures, nonstationarity, simulta- neous diagonalization, temporal correlations 1. Introduction Blind source separation (BSS) is a fundamental prob- lem that is encountered in many practical applications such as telecommunications, array signal processing, image processing, speech processing (cocktail party problem), and biomedical signal analysis where mul- tiple sensors are involved. In its simplest form, the -dimensional observation vector is as- sumed to be generated by (1) where is the unknown mixing matrix, is the -dimensional source vector (which is also unknown and ), and is the additive noise vector that is statistically independent of . The task of BSS is to estimate the mixing matrix (or its pseudo-inverse, that is referred to as the demixing matrix), given only a finite number of observation data , . Two indeter- minacies cannot be resolved in BSS without any prior knowledge. They include scaling and permutation am- biguities. Thus if the estimate of the mixing matrix, satisfies where is the global transformation which combines the mixing and demixing system, is some permutation matrix, and