Optimal designs for estimating pairs of coefficients in Fourier regression models

In the common Fourier regression model we investigate the optimal design problem for estimating pairs of the coefficients, where the explanatory variable varies in the interval [i¼; ¼]. L-optimal designs are considered and for many important cases L-optimal designs can be found explicitly, where the complexity of the solution depends on the degree of the trigonometric regression model and the order of the terms for which the pair of the coe±cients has to be estimated.