Accurate estimation of amplitude, frequency, and phase of harmonic signal components using an FFT

Abstract

The signal analyzed using an FFT is seldom identical to the true signal. This can result in inaccurate estimates of amplitude, frequency, and phase of harmonic signals. Using an extension of a method described earlier [J. C. Burgess, “On digital spectral analysis of periodic signals,” J. Acoust. Soc. Am. 58, 556–567 (1975)], it is possible to estimate the true amplitude, frequency, and phase of a harmonic signal with good accuracy. For example, acoustic intensity measurements may require determining the phase difference between two harmonic signals of the same amplitude and frequency. Using the method described, this phase difference often can be estimated with an error less than 0.01%. The method requires use of an optimum data window that can be expressed as a Fourier series having only a few nonzero coefficients.