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Recently, a generalized noise reduction scheme has been proposed, called the Spatially Preprocessed, Speech Distortion Weighted, Multichannel Wiener Filter (SP-SDW-MWF). It encompasses the Generalized Sidelobe Canceller (GSC) and a multichannel Wiener filtering technique as extreme cases. Compared with the widely studied GSC with Quadratic Inequality Constraint (QIC-GSC), the SP-SDW-MWF achieves a better noise reduction performance for a given maximum speech distortion level. We develop a low-cost, stochastic gradient implementation of the SP-SDW-MWF. To speed up convergence and reduce computational complexity, the algorithm is implemented in the frequency domain. Experimental results with a behind-the-ear hearing aid show that the proposed frequency-domain stochastic gradient algorithm preserves the benefit of the exact SP-SDW-MWF over the QIC-GSC, while its computational cost is comparable to the least mean square-based scaled projection algorithm for QIC-GSC.