Convergence properties of an adaptive Fourier analyzer

A PLL-like adaptive Fourier analyzer (AFA) was proposed which has shown excellent performance in practical applications. The convergence analysis of this AFA is extremely difficult, and until now theoretical results have not been available. In this paper a modified version of the original AFA is proposed. The new version preserves the effectiveness of the original AFA, and its convergence properties can be exactly analyzed. Sufficient conditions are presented for the exponential stability, and the absolutely monotone convergence, as a function of the harmonic content of the input signal. The speed of the convergence is also estimated, and the effect of the noise and of unmodeled periodic components are analyzed.