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Multichannel blind deconvolution (MCBD) algorithms are known to suffer from an extensive computational complexity problem, which makes them impractical for blind source separation (BSS) of speech and audio signals. This problem is even more serious with noncausal MCBD algorithms that must be used in many frequently occurring BSS setups. In this paper, we propose a novel frequency domain algorithm for the efficient implementation of noncausal multichannel blind deconvolution. A block-wise formulation is first developed for filtering and adaptation of filter coefficients. Based on this formulation, we present a modified overlap-save procedure for noncausal filtering in the frequency domain. We also derive update equations for training both causal and anti-causal filters in the frequency domain. Our evaluations indicate that the proposed frequency domain implementation reduces the computational requirements of the algorithm by a factor of more than 100 for typical filter lengths used in blind speech separation. The algorithm is employed successfully for the separation of speech mixtures in a reverberant room. Simulation results demonstrate the superior performance of the proposed algorithm over causal MCBD algorithms in many potential source and microphone positions. It is shown that in BSS problems, causal MCBD algorithms with center-spike initialization do not always converge to a delayed form of the desired noncausal solution, further revealing the need for an efficient noncausal MCBD algorithm.