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.

[1]  Olivier Besson,et al.  On estimating the frequency of a sinusoid in autoregressive multiplicative noise , 1993, Signal Process..

[2]  Georgios B. Giannakis,et al.  Statistical tests for presence of cyclostationarity , 1994, IEEE Trans. Signal Process..

[3]  Roger F. Dwyer,et al.  Fourth‐order spectra of Gaussian amplitude‐modulated sinusoids , 1991 .

[4]  M. Rosenblatt,et al.  Estimation of the Bispectrum , 1965 .

[5]  Ananthram Swami,et al.  Multiplicative noise models: parameter estimation using cumulants , 1994, Fifth ASSP Workshop on Spectrum Estimation and Modeling.

[6]  Petre Stoica,et al.  Sinusoidal signals with random amplitude: least-squares estimators and their statistical analysis , 1995, IEEE Trans. Signal Process..

[7]  Chen Zhao-guo.  Consistent estimates for hidden frequencies in a linear process , 1988, Advances in Applied Probability.

[8]  Georgios B. Giannakis,et al.  Harmonics in multiplicative and additive noise: parameter estimation using cyclic statistics , 1995, IEEE Trans. Signal Process..

[9]  Georgios B. Giannakis,et al.  Asymptotic theory of mixed time averages and k th-order cyclic-moment and cumulant statistics , 1995, IEEE Trans. Inf. Theory.

[10]  Georgios B. Giannakis,et al.  On estimating random amplitude-modulated harmonics using higher order spectra , 1994 .

[11]  D. Brillinger.  Time Series: Data Analysis and Theory. , 1981 .

[12]  E. Parzen.  On Consistent Estimates of the Spectrum of a Stationary Time Series , 1957 .