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Period estimation for adaptive reconstruction of (quasi‐) periodic signals
Author(s) -
Rairan Danilo,
Garzon Max H.
Publication year - 2015
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2458
Subject(s) - sampling (signal processing) , algorithm , signal (programming language) , computer science , a priori and a posteriori , signal processing , harmonics , range (aeronautics) , coherent sampling , fourier transform , signal reconstruction , fourier series , discrete time signal , periodic function , mathematics , signal transfer function , analog signal , digital signal processing , telecommunications , transmission (telecommunications) , computer vision , filter (signal processing) , philosophy , materials science , voltage , mathematical analysis , composite material , epistemology , quantum mechanics , programming language , physics , computer hardware
SUMMARY Signal reconstruction from sampling data is an important problem in signal processing and system identification. A large variety of signals of current interest do not satisfy common assumptions about fitting certain models, are too dynamic, have an unknown period, and/or are computationally infeasible, so that current methods may be inappropriate for their identification and reconstruction. The discrete Fourier transform can be used to estimate the period of a discrete time signal when the first harmonic of its Fourier expansion has the maximum amplitude among all harmonics, the number of data points in a period is even, and a multiple of the sampling period matches the true period. The signal is generally impossible to reconstruct accurately without a priori knowledge of the period, or its inverse, the frequency. We address this problem with two efficient algorithms that are model‐free, data‐based, and dynamically adaptive for signal processing and provide estimates of the period that are guaranteed to be within a maximum error of the true period in the order of the sampling period of the signal, usually in real time. In addition, we present theoretical guarantees and experimental evidence of the quality of the algorithms in practice with very competitive results, even when the data is noisy, dynamic, require real‐time estimates, and even for quasi periodic signals. The results thus extend the three range of applicability of the FFT and sampling theorem for signal reconstruction and illustrate the applicability of these algorithms to other problems, such as power systems and sunspot prediction. Copyright © 2013 John Wiley & Sons, Ltd.