Resolution bias errors in spectral density, frequency response and coherence function measurements, III: Application to second-order systems (white noise excitation)

Abstract

A general theory of spectral estimation given in a previous paper is applied to second-order systems such as a simple spring-mass system where either the displacement, velocity or acceleration of the vibrating mass may be considered as the output signals. By means of approximate formulas, an extensive bias error discussion of frequency response, output power spectral density and coherence estimates is given, which clarifies characteristic differences between spectral estimators obtained with the rectangular window on the one hand and the Hanning window (or another continuous window) on the other hand. In particular, characteristic coherence notches in the measurement of resonance systems, as reported in the literature, are explained from first principles. All of the theoretical predictions are verified experimentally to great accuracy by using electrical LRC-resonance circuits which are equivalent to the respective mechanical systems.