The objective of this thesis is to study the demodulation of narrowband radio frequency signals by aliasing sampling in order to reduce the sampling rate. The spectrum can be recreated at the lower frequency position by aliasing sampling. However, if the sampling rate is deviated from the desired one, error will occur. The sensitivity to the frequency error of aliasing sampling is studied. One main reason of the deviation of the sampling rate is the frequency drifting of the local oscillator. Being able to compensate the oscillator drifting errors inexpensively, automatic frequency control (AFC) loops are important at receivers. Two major digital AFC algorithms are studied. One is the Phase method AFC, and the other is the Magnitude method AFC. Study indicates that both methods perform almost equally well. One adaptive AFC algorithm is also proposed. The scheme of the adaptive AFC algorithm is to use Upper-bound and Lower-bound techniques to squeeze the frequency errors. It is shown that the adaptive AFC algorithm can achieve up to 20 dB average signal-to-noise power ratio over the Magnitude method AFC under a noisy environment.