1. A method for reducing noise signals and background signals in a speech-processing system, comprising: adaptively filtering an audio input signal, using a filter, 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; where the absolute values of the coefficients are continuously reduced by a plurality of reduction parameters; where the prediction output signal as a prediction of the audio input signal with reduced noise is used as an input signal for a second filter to generate a second prediction; and where the second filter comprises a prediction filter having a second filter with a set of second coefficients, wherein a learning rate to adapt the coefficients is selected that is several powers of ten less than a learning rate of the first filter.