Algorithm for Fourier coefficient estimation

This study deals with the estimation of amplitude and phase of an analogue multi-harmonic band-limited signal from irregularly spaced sampling values. To this end, assuming the signal fundamental frequency is known in advance (i.e. estimated at an independent stage), a complexity-reduced algorithm for signal reconstruction in time domain is proposed. The reduction in complexity is achieved owing to completely new analytical and summarised expressions that enable a quick estimation at a low numerical error. The proposed algorithm can be applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise root mean square measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The authors investigate the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.