Some estimation problems for harmonics in multiplicative and additive noise

The large sample properties of the finite Fourier transform for generally complex processes are established under certain mixing conditions. The uniformly convergent rate of the sample cyclic-moments of cyclostationary processes is obtained. For harmonics in multiplicative and additive noise, the statistical properties of the sample cyclic-moments are obtained. As an important consequence, some procedures based on different order cyclic-moments are offered for estimating the harmonics component number and frequencies, and the strong convergence and convergence rates of the estimators are obtained.