Iteration of mappings and fixed points in mixed spectrum analysis

Here we will analyze the mixed spectrum model for , where p is not necessarily known and, for each , is an unknown constant , is an unknown frequency with value in and the phase is a random variable uniformly distributed in independent of each other and of the noise component. The authors assume that the noise component is Gaussian white noise such that . Observe that the process is not Gaussian. Here the authors present a recursive method of updating parameters for estimating the frequencies , . The cosines of the frequencies are obtained as attracting fixed points of a certain map.