Improving Frequency Resolution of Discrete Spectra: Algorithms of Three-node Interpolation

Discrete spectra can be used to measure frequencies of signal components. Such a measurement consists in digitising the signal, performing windowing of the signal samples and computing their discrete Fourier spectrum. Frequencies of individual signal components can be evaluated from their locations in the discrete spectrum magnitude with resolution limited by the number of processed samples. The book describes interpolation algorithms based on three bins of the discrete Fourier spectrum, allowing to increase frequency resolution of such measurements by a few orders of magnitude at the expense of computing one formula. Studies of the dependence of the algorithm efficiency on windowing, noise, interference and exponential decay of the signal are included. The algorithms of discrete spectra interpolation studied in this book may find applications in scientific and industrial systems requiring real-time, high resolution frequency measurements, based on small sample sets. In particular, they can be a computation-saving replacement of the zero-padding technique. The algorithms have been used for years at CERN in systems measuring characteristic frequencies of particle beam motion.