The determination of the frequencies of a multisine signal can be very important at diferent signal processing tasks, like vibration measurements and active noise control related to rotating machinery and calibration equipment. Adaptive Fourier Analyzers have been developedfor 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 the correct use we have to have pre-estimation 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 non-tolerable delay in the operation. In this paper, a new fast fuzzy logic supported anytime frequency range estimation procedure is proposed which makes 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.