The ${Delta};V_{10}$ or 10-Hz flicker index, as a common method of measurement of voltage flicker severity in power systems, requires a high computational cost and a large amount of memory. In this paper, for measuring the ${Delta};V_{10}$ index, a new method based on the Adaline (adaptive linear neuron) system, the FFT (fast Fourier transform), and the PSO (particle swarm optimization) algorithm is proposed. In this method, for reducing the sampling frequency, calculations are carried out on the envelope of a power system voltage that contains a flicker component. Extracting the envelope of the voltage is implemented by the Adaline system. In addition, in order to increase the accuracy in computing the flicker components, the PSO algorithm is used for reducing the spectral leakage error in the FFT calculations. Therefore, the proposed method has a lower computational cost in FFT computation due to the use of a smaller sampling window. It also requires less memory since it uses the envelope of the power system voltage. Moreover, it shows more accuracy because the PSO algorithm is used in the determination of the flicker frequency and the corresponding amplitude. The sensitivity of the proposed method with respect to the main frequency drift is very low. The proposed algorithm is evaluated by simulations. The validity of the simulations is proven by the implementation of the algorithm with an ARM microcontroller-based digital system. Finally, its function is evaluated with real-time measurements.