Parameters Estimation of Complex Multitone Signal in the DFT Domain

In a previous paper, a method was introduced that used a system of linear equations to determine the frequency and the complex amplitude of a complex single tone signal. The system of linear equations was derived from the model of a complex single tone in the DFT domain and was used as parameters estimator in noisy conditions. In this paper, this approach is extended to a complex multitone signal. As for the complex single tone case, the parameters value is determine from the solution of systems of linear equations and the method is directly applied for parameters estimation in noisy conditions. An analysis of the estimators is provided, including the case of closely spaced frequencies, and criteria and procedures for the appropriate selection of the DFT samples are presented.