The concepts of filtering and sampling of the voltage and current signals of the power system are introduced for harmonic analysis using the Fast Fourier Transform (FFT) algorithm. Next, we discuss the application of a multi-rate digital signal processing technique to a harmonic analysis and cover the design of a polyphase decimation finite impulse response (FIR) filter for use as an anti-aliasing filter in oversampling applications. The implementation of this filter together with an FFT by a digital signal processor is described, and the results of the synchronization tests of the algorithms are presented. The instrument used to implement these techniques is an advanced data acquisition and parallel processing system specifically aimed at continuous monitoring of the real-time energy system signal.