Removal of periodic interference using the Farey bases

Many sonar signals of interest and interferences have periodic structure, which is represented in the frequency domain as tones at multiples of the fundamental frequency. Estimation of the fundamental frequency (or its inverse, the period) is important for inference on signals of interest and for rejection of periodic interferences. Period estimation, however, is often hindered by strong tones obscuring harmonic structure and by the varying number of harmonics associated with each potential period. A combined detection/estimation approach is presented to address these issues under very general assumptions about the statistical characterization of the periodic signal and noise. The resulting algorithm efficiently estimates the period of a signal by exploiting Farey bases (an economical representation of periodic signals), the sign test, and the generalized likelihood ratio principle. Application of the technique to real data illustrates its effectiveness at removing a persistent periodic interference.