An ultra-precise fast fourier transform

Abstract The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating computationally efficient estimate the frequency content time series. Its limitations include: (1) information only provided at discrete steps, so further calculation, for example interpolation, often used to obtain improved estimates peak frequencies and amplitudes; (2) ‘energy' from spectral peaks may ‘leak' into adjacent frequencies, potentially causing lower amplitude be distorted or hidden; (3) FFT, like many other DSP algorithms, approximation continuous mathematics. This paper describes new FFT calculation which uses two windowing functions, derived Prism Signal Processing. Separate results are obtained each function applied data set. Calculations based on yields high precision location (frequency), phase. technique addresses as follows: parameters calculated directly, unrestricted by step discretization; functions have narrowband characteristics attenuate localize leakage; incorporate Romberg Integration mechanism overcome discrete/continuous approximation.