A note on the sampling distribution of coherence estimate for the detection of periodic signals

The sampling distribution of coherence estimate between one random and one periodic signal was shown to follow a noncentral beta distribution. This result is useful in further investigations to obtain the moments of the estimate. The plots of the probability density function (pdf) also provide an indication of its bias and random variability. Alternative algorithms for expressing this distribution were developed based on central and noncentral F pdf. The latter is exact and the first, an approximation which was shown to be suitable in practical situations. The zero-coherence case was obtained as special case when the noncentrality parameter is zero.