Abstract: A speech separating digital signal processing system and algorithms for implementing speech separation combine beam-forming with residual noise suppression, such as computational auditory scene analysis (CASA) using a beam-former that has a primary lobe steered toward the source of speech by a control value generated from an adaptive filter. An estimator estimates the ambient noise and provides an input to the residual noise suppressor, and a post-filter may be used to noise-reduce the output of the estimator using a time-varying filter that compares two or more outputs of the beam-former with a quasi-stationary model of the speech and ambient noise.