Period estimation for adaptive reconstruction of (quasi-) periodic signals

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