Superfast fourier transform and its application in dynamic calibration of transducers

Abstract It is well known that discrete Fourier transform (DFT) and fast Fourier transform (FFT) play an important role in signal processing. But DFT multiplied by sampling period T is just a zero-order approximation of Fourier transform (FT). Therefore, in order to raise the precision of signal processing we have theoretically to reduce the sampling period, but in fact this would at least lead to much greater error because of the accumulation of quantification error in the orignal signal. In this paper, a new method, instead of the zero-order approximation method, is presented and discussed in detail, in which FT takes the form of a product of DFT and weighted complex factors varying only with frequency points, and FFT could be used to raise the speed of computation. The new method greatly increases accuracy with the same sampling points. In other words, it makes the number of necessary sampling points less thus increasing the speed of computation (over fifteen times) with the same accuracy. For this reason, the new method is called superfast Fourier transform (SFT). Applications of SFT are also discussed and some useful conclusions are reached.