Estimation of complex Fourier coefficients

The estimation of complex Fourier coefficients of periodic functions from additively error disturbed observations is discussed. This is the first step of most methods for estimating the parameters of linear dynamic systems from noise disturbed responses to periodic perturbation signals. In this type of estimation problem the period is known. The complex Fourier coefficient estimator is also the first step of procedures for reconstructing periodic images from noisy observations. In these problems the period is usually unknown; the Fourier coefficients and the period have to be estimated jointly. The estimators for both types of problems are proposed, which are complex valued estimators. The real and imaginary part of the complex valued parameters to be estimated are not treated as separate real parameters. Statistical and numerical properties of the proposed estimators are described.