A method to perform adaptive channel filtering on a Radio Frequency (RF) bursts in a cellular wireless communication system. This method first filters an input signal with a first stage filter having a first bandwidth to produce a first stage output signal. Then the first stage output signal is filtered with a second stage filter having a second bandwidth narrower than that of the first stage filter to produce a multi-stage output signal. A comparison between first stage performance measurements and multi-stage performance measurements determine the mode of operation of the adaptive multistage filter. A first mode of operation, selected when the first stage performance measurement compares favorably with the second stage performance measurement, selects the output of the first stage filter as the output of the multi-stage filter. Otherwise, a second mode of operation selects the output of the second stage filter as the output of the multi-stage filter.