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Reply Review of Dr. Y. Xiang's calculationWe read with great interest Dr. Yong Xiang's letter about our paper ''Novel cyclostationary based blind source separation algorithm using second order statistical properties: theory and application to the bearing defect diagnosis''. It appears to us that the calculation by which Dr. Yong Xiang demonstrates that our criterion does not hold suffers an error that leads him to improper conclusions. The criterion we proposed does lead to perfect separation, as shown in what follows.The criterion Dr. Xiang proposes is a generalisation of ours which differs from it by being more formally expressed and being implemented by a recursive algorithm. We are pleased Dr. Xiang thinks our criterion is worth being extended so. These enhancements could be submitted to MSSP as a regular paper.Dr. Xiang computed the derivative of our separation criterion. This criterion depends on two coefficients a(y) and b(y). Complete separation means filtering out the stationary source, which leads to b(y opt ) ¼ 0. Dr. Xiang then shows that this assertion leads to a main contradiction and thus proves our criterion to be nonoptimal. In fact, it escaped from Dr. Xiang's attention that not only b(y opt ) ¼ 0 but also da/dy(y opt ) ¼ 0, so that from Eq. (9) his assertions are incorrect. We demonstrate this by the following calculation.Let us focus on the 2 * 2 case, as in the original paper. We wish to retreive the cyclostationary source on the first component z 1 (t) of z(t), the estimates vector. This first component is a linear combination of the sources, with coefficients a(y) and b(y):0888-3270/$ -see front matter r