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Active noise control (ANC) requires a controller with a small delay. However, in most ANC applications, this delay is significant due to the typically low sample rate, the anti-aliasing (AA), and reconstruction filters (RC) of the analog to digital (AD) and digital to analog (DA) converters. This delay can be reduced by increasing the sampling frequency at the expense of a significant increase in computational complexity. Sigma-delta AD and DA converters work at high sampling frequencies, but their use in ANC is limited due to the delay of AA and RC filters. This work proposes removing the AA and RC filters of the sigma-delta converters and using the oversampled signals directly in an ANC system. This proposal allows the ANC system to be implemented at a large sample frequency but using signals with fewer bits per sample (word-length). This is the first short-word length implementation of the least mean squares (LMS) algorithm to the authors’ knowledge. Gains of up to 6 times may be achieved in the computational complexity when compared with a long-word length implementation. Theoretical and simulation results validate the current solution. [ABSTRACT FROM AUTHOR]