AbstractThis paper discusses the identification of an asynchronously generated unknown pattern buried in stationary noise. The historical background of the problem is described and it is pointed out that the existence in principle of a solution of this problem is not known. The statistical moment function of the ensemble of observation is defined in the frequency domain and the discussion is carried out in the frequency domain. The pattern is represented in the frequency domain in polar coordinates, and identification is attempted separately for amplitude and phase. The unknown pattern is shown to be identified by utilizing information on the first and the second moment functions of the samples. It is shown that the amplitude term of the solution can be represented quite simply for white noise. It is further shown (even when the noise is not white but is normally distributed) that the amplitude term of the solution can be represented relatively simply by using the third‐order moment function of the sample. It is shown that the phase term of the solution is given as a solution of a certain system of equations. When the characteristic function of the probability density of the fluctuation in position of the pattern is a positive real function, the representation becomes simple by using the first‐order moment function of the sam