New Procedure for Estimation of Amplitude and Phase of Analog Multiharmonic Signal Based on the Differential Irregular Samples

Abstract

© 2014, Springer Science+Business Media New York. 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 that the signal fundamental frequency is known beforehand (i.e., estimated in an independent stage), a complexity-reduced scheme is proposed here. The reduction in complexity is achieved owing to completely new analytical and summarised expressions that enable quick estimation at a low numerical error. The proposed algorithm for the calculation of the unknown parameters requires O((2M)2) flops, while the straightforward solution of the obtained equations takes O((2M)3) flops, where M is number of harmonic coefficients. It is proved that the estimation performance of the proposed algorithm can attain Cramer-Rao lower bound (CRLB) for sufficiently high signal-to-noise ratios. It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The paper investigates the errors related to the signal parameter estimation, and computer simulation demonstrates the accuracy of these algorithms.