An adaptive signal processing system eliminates noise from input signals while retaining desired signal content, such as speech. The resulting low noise output signal delivers improved clarity and intelligibility. The low noise output signal also improves the performance of subsequent signal processing systems, including speech recognition systems. An adaptive beamformer in the signal processing system consistently updates beamforming signal weights in response to changing microphone signal conditions. The adaptive weights emphasize the contribution of high energy microphone signals to the beamformed output signal. In addition, adaptive noise cancellation logic removes residual noise from the beamformed output signal based on a noise estimate derived from the microphone input signals.