ACCURATE AND FAST ESTIMATION OF THE FOURIER COEFFICIENTS OF PERIODIC SIGNALS DISTURBED BY TRENDS

In this paper, a linear least-squares estimator is presented for the e stimation of the Fourier coefficients and trend components of a period ic time series disturbed by a trend, In opposition to existing methods , the removal of the trend is not separated from the estimation of the Fourier coefficients, Based on the mathematical description of the pr oposed algorithm, a computationally efficient implementation is given, It is demonstrated under some weak assumptions (mixing condition on t he measurement noise) that the estimates of the Fourier coefficients a re consistent (converge to the true Fourier coefficients of the period ic signal), asymptotically efficient (lowest possible uncertainty), an d asymptotically normally distributed, Moreover, using simulations it is shown that the asymptotic properties of the estimator are reached f or practical measurement problems, Finally, the estimator is applied t o the measured load current and voltage of a traction battery.