An Observer-Based Adaptive Fourier Analysis [Tips & Tricks]

Recently, an observer-based algorithm was reviewed that is able to perform recursive sliding discrete Fourier transform (SDFT) [1]. DFT is the basic algorithm used for Fourier analysis [2], but it provides unbiased estimates only if the sampling is coherent, i.e., the ratio of the sampling frequency f_s and the input signal frequency f_in is a rational number. Coherent sampling of real-life periodic signals (e.g., mains voltage) can only be achieved if f_in and f_s are synchronized.