A method for processing a radio signal which may include a narrowband signal or a wideband signal or both, comprises the steps of receiving the radio signal, initially processing the radio signal using a narrowband filter, switching to a wideband filter for further processing of the radio signal, determining if the wideband signal is acquired, and if the wideband signal is not acquired, alternating between narrowband filter processing for a narrowband filter hold time and wideband filter processing for a wideband filter hold time, where the narrowband filter hold time is gradually increased until a predetermined maximum time limit is reached. If the wideband signal is acquired, the narrowband filter hold time can be set to a predetermined minimum time limit. Receivers which implement the method are also provided.