A note on the coherence-based signal-to-noise ratio estimation in systems with periodic inputs

Coherence plays a very important role in linear systems analysis, since, in addition to quantify the similarity between signals, it is related to other quantities of interest, such as the signal-to-noise ratio (SNR). The sampling distribution of coherence estimates between Gaussian signals is well established, and hence, in this particular case, the statistics of SNR can be readily found if it is calculated from coherence estimates. However, in some applications, one of the signals is periodic, leading to a different coherence sampling distribution, which has been recently investigated. This work aims at developing analytical expressions for bias, variance and the probability density function of coherence-based SNR estimates under this particular assumption. Routines for obtaining this latter as well as critical values of the estimates are also provided.