This paper presents a new, analytically driven frequency weighted model order reduction method. The method is grounded on the Fourier-based decomposition of a high-order state space model. The method is designed for discrete-time systems, but it can be easily applied to continuous-time ones. The main advantage of the proposed algorithm is a class of quadratic time complexity as compared to the cubic one for the classical frequency weighted method, the major feature resulting from the application of analytical methods for calculation of factorizations for controllability and observability Gramians. The simulation experiment confirms the effectiveness of the proposed method both in terms of high modeling accuracy and low computational cost. (C) 2017 Elsevier Ltd. All rights reserved.