Automatic frequency control via digital filtering

This paper presents a unique digital realization of an automatic frequency control (AFC) for tracking signals that are slowly drifting in frequency. The frequency discriminator consists of two stagger-tuned digital filters, whose squared outputs are differenced and averaged. The frequency tracking is performed by changing the centers of the digital filters and hence the discriminator characteristic. This can be done easily by only a few cosine calculations. The digital loop filter, operating at a much slower sampling rate than the discriminator filters, is designed to minimize probability of loss of lock. Zero mean white additive Gaussian noise is inserted in the linearized loop to account for both the additive channel noise and the short-term signal instabilities. The variance of the frequency estimate is then calculated. The only assumption made on the frequency drift process is that the drift rate be less than a given value. A worst-case analysis is performed to obtain the largest possible mean frequency error. Loss of lock is said to occur when the actual frequency error is greater than the width of the linear portion of the discriminator characteristic.