A statistical theory of signal coherence

A periodic signal can be perfectly predicted far into the future since it p erfectly repeats every period. There is always some variation in the wavefo rm over time for signals which are labeled as periodic but which are not tr uly deterministic. A formal definition is presented in this paper for such a varying periodic signal and the properties of such a class of signals are exploited. A measure called a signal coherence function of the amount of r andom variation in each Fourier component of the signal is defined and its statistical properties are developed. This signal coherence function is ver y different from the coherence function between two stationary signals. The method is applied to a digitized record of an acoustic signal generated by a boat in a bay in the Baltic Sea south of Stockholm, Sweden.