An ultra-precise Fast Fourier Transform

Abstract

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies, amplitudes and phases; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase while suppressing spectral leakage.