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For several years, contrast-based blind source separation (BSS) has been successfully used in several areas, including radiocommunications. A functional approach relying on differential calculus theory is proposed, aiming at analyzing asymptotic performances of BSS contrast criteria: the variance of the estimated separating matrix is expressed as a function of that of estimated cumulants. As an example, the paper focuses on three widely used fourth order (FO) contrast criteria. This allows the behavior of these three separators to be quantified for large samples.