Strong ergodicity conditions for the nth-order moment (cumulant) of multiple sinusoids

Abstract

We derive sufficient conditions for stationarity and strong ergodicity of multiple sinusoids, both for the real-valued as well as for the complex-valued cases, and for any kind of postulated phase coupling law. We derive bounds on the rate of convergence of the sample estimator, and we establish ergodicity conditions in the presence of additive as well as multiplicative noise. We show that record segmentation does not lead to consistent estimates; finally, we establish that lack of ergodicity does not imply lack of parameter identifiability based on the sample estimator.