REFERENCING THE PHASE TO THE CENTER OF THE SPECTRAL WINDOW - WHY

In harmonic analysis with fast Fourier transforms, referencing the pha se at the centre of the spectral window is a useful means of perceivin g a problem and conceiving a solution because, algebraically speaking, the phase can be referenced anywhere. The Cramer-Rao bound is used to demonstrate that the phase reconstruction error is minimum at the cen tre of the data buffer acquired with a rectangular window. In more gen eral terms, in the presence of a frequency- and amplitude-modulated si nusoidal signal contaminated with noise, it is suggested that the spec tral estimation gives the amplitude, frequency and phase of the signal as it passes through the middle of the observation window. It is at t he centre of this window that signal reconstruction is most accurate. Furthermore, presenting a phase value referenced to another location o ften makes the equations relating the phase more complicated to formul ate. Different examples of applications are provided along with the re asons why Hydro-Quebec has standardised this reference for its turbine -generator monitoring system. (C) 1997 Academic Press Limited