A receiver for efficient wireless communications in the presence of frequency errors in a radio frequency received signal is disclosed. The receiver comprising a receiver channel, a wide band frequency acquisition mode, automatic frequency control, a narrow band demodulation mode and a demodulator. The receiver channel has a variable bandwidth and an approximately fixed receiver mid-channel frequency. The wide band frequency acquisition mode comprises a wide channel filter which initially defines the bandwidth to be greater than the frequency error in the received signal and wherein the frequency error is determined by comparing the received signal frequency to the receiver mid-channel frequency. The automatic frequency control comprises at least one frequency adjustable local oscillator which it adjusts based upon the frequency error such that the frequency difference between the receiver mid-channel frequency and the received signal is made negligible, thereby approximately centering the received signal within the bandwidth in the wide band frequency acquisition mode. The narrow band demodulation mode comprises a narrower channel filter which narrows the bandwidth of the receiver channel with respect to the wide band frequency acquisition mode and maintains approximately the same receiver mid-channel frequency. The demodulator demodulates the received signal in the narrow band demodulation mode. Automatic frequency control and bandwidth selection using-adaptive digital signal processing based filters is also disclosed. In this case instead of the local oscillator being adjusted to tune in the desired signal, the filter center frequency is adapted.