An adaptive filter is programmed with an algorithm based on a normalized Least Mean Squares (nLMS) algorithm that adapts each sample time. The algorithm is modified to be more efficient in a variety of DSPs by computing multiple errors, one per sample, before updating coefficients. The update equation utilizes the multiple errors to achieve adaptation at a similar performance to known nLMS algorithms that adapt each sample time but without the instability that is observed in low echo-to-near-end-noise ratio (ENR) input conditions. Varying the relaxation step size prevents divergence. The DSP utilizes either one or more MAC units.