Fast Anytime Fuzzy Fourier Estimation of Multisine Signals

The determination of the frequencies (and amplitude components) of a multisine signal can be very important for different signal processing tasks like vibration measurements and active noise control related to rotating machinery and calibration equipment. Adaptive Fourier analyzers have been developed for measuring periodic signals with unknown or changing fundamental frequency. Higher frequency applications have limitations since the computational complexity of these analyzers are relatively high as the number of harmonic components to be measured (or suppressed) is usually above 50. Recently, a fast filter-bank structure has been proposed for adaptive Fourier analysis based on the combination of the concept of transform-domain signal processing and the adaptation of a simple linear combiner. It results in the reduction of the above computational complexity; however, for correct use, we have to have preestimation about the range of the fundamental frequency to be able to set the applied single-input-multiple-output filter banks, which, in many cases, causes significant and possibly nontolerable delay in the operation. In this paper, a new fast fuzzy-logic-supported anytime frequency range-estimation procedure is proposed, which makes it possible to execute the frequency estimation after one quarter of the period of the unknown signal, i.e., the adaptation and Fourier analysis can be performed without any delay.