In this paper we present the model of digital stochastic DFT processor. Compared to the classical DFT/FFT processors, the proposed model has two advantages: first, it is much simpler and cheaper to implement, and second, it allows us to compute individual DFT components either in isolation or in parallel. In order to prove the validity of our model, we have simulated the measurement of reactive power and energy. In addition, we have conducted several experiments under field and laboratory conditions. The obtained results have shown that reactive power and energy can be measured with an accuracy of several ppm.