A fast filter-bank for adaptive Fourier analysis

Adaptive Fourier analyzers have been developed for measuring periodic signals with unknown or changing fundamental frequency. Typical applications are vibration measurements and active noise control related to rotating machinery and calibration equipment that can avoid the changes of the line frequency by adaptation. Higher frequency applications have limitations since the computational complexity of these analyzers are relatively high as the number of the harmonic components to be measured (or suppressed) is usually above 50. In this paper, based on the concept of transformed domain signal processing, a fast filter-bank structure is proposed to reduce the above computational complexity. The first step of the suggested solution is the application of the filter-bank version of the fast Fourier transform or any other fast transformations that convert input data into the transformed domain. These fast transform structures operate as single-input multiple-output filter-banks, however, they can not be adapted since their efficiency is due to their special symmetry. As a second step, the adaptation of the filter-bank is performed at the transform structure's output by adapting a simple linear combiner to the fundamental frequency of the periodic signal to be processed.