Transformée de Fourier rapide par quart de période

Abstract
Any periodical signal can be decomposed in Fourier series. When the number of harmonics is limited and the signal period in known, the series coefficient calculation can be done exactly by simple additions or substractions of a limited number of sampled values. For each harmonic, four sample are taken is each harmonic period. The first advantage is to remove every product in the computation. The second advantage is to obtain independent filters that only let through their harmonic and some multiple harmonics. By setting up one filter per harmonic, it is easy to find any coefficient. Each filter requires its own sampling clock ; so, sampling is asynchronous for a set of filters. When harmonics are numerous, the sampling device is tricky to carry out.