This invention relates to a device for and method of implementing an ambient noise-cancellation (ANC) circuit that uses digital processing whereby a signal indicative of the ambient noise is converted to digital form, filtered, using a fixed or adaptive digital filter, and then converted back to analog before sending it to an ear-proximate speaker. In order to address the time delays associated with such processing operations, the analog-to-digital converter used is associated with a down-sampler, and the arrangement is such that a first part of the filtering is implemented by the down-sampler, and a second part of the filtering is implemented by the digital filter. This reduces group delay by configuring a down-sampler associated with the front end of the analog-to-digital converter to incorporate selected filter characteristics of the overall ANC filter response, and modifying the subsequent filtering processing stage to compensate for this.