Systems, methods, and machine-readable storage devices that receive an input signal representing audio captured using a microphone. The input signal includes portions that represent acoustic output from one or more audio sources, and a portion that represents other acoustic energy in the environment. A frequency domain representation of the input signal is iteratively modified to substantially reduce effects due to all but a selected one of the portions, from which an estimate of the power spectral density, PSD, of the selected portion is determined. Based upon the estimated PSD a noise or echo component is reduced, or a replacement noise is provided. The iterative modification involves a diagonalization of the cross-spectral density matrix to remove content coherent with a first audio input from the auto and cross-spectra of other signals.