Optimal designs for estimating individual coefficients in Fourier regression models

In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coefficients, where the explanatory variable varies in the interval [-a ,a] ; 0 < a < t. It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many cases optimal designs can be found explicitly, where the complexity of the solution depends on the value of the parameter a and the order of the term, for which the corresponding coefficient has to be estimated.