The paper is devoted to H2-optimization problem for LTI systems with scalar control and external disturbance and with multivariate no noisy measurement signal. This problem has a significant specific feature: its solution is no unique. Besides, the absence of the measurement noise makes this problem irregular with respect to standards of H-theory. To obtain the numerical solution, one can use traditional approaches based on the various modifications of 2-Riccati or LMI technique. Nevertheless, to increase a computational efficiency of the synthesis, it is quite appropriate to use a special spectral approach to the problem in frequency domain. A theory of this issue is presented and computational scheme is proposed for practical implementation.