1. A method for reducing noise signals and background signals in a speech-processing system, comprising: adaptively filtering, using a first filter, an audio input signal to generate a prediction output signal using a plurality of coefficients to generate a plurality of prediction errors and generating an error from the plurality of prediction errors, where the prediction output signal is the sum of the plurality of prediction errors; using a multiplier to weight the audio input signal or to weight the prediction output signal by a weighting factor smaller than one to generate a weighted signal; and using an adder to add the weighted signal to the prediction output signal to generate a noise-reduced audio output signal.