Fourier Coefficient Estimation Based Differential Values of the Processed Signal

摘要

This paper is concerned with the estimation of amplitude and phase of an analog multi-harmonic signal based on a series of differential values of the signal. To this end, assuming the signal fundamental frequency is known before hand (i.e., estimated in an independent stage), a complexity-reduced scheme is proposed here, based on the matrix method classically used to estimate the Fourier coefficients. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. It is 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 (rms) measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.