Error analysis of spectral estimates with application to the measurement of acoustic parameters using random sound fields in ducts

Abstract

Several methods have been proposed using multiple-point pressure measurement of random sound fields in ducts to determine acoustic properties of materials and systems. This paper presents an error analysis of the spectral estimates used in these techniques. Expressions for the normal acoustic absorption coefficient and impedance are derived for a random sound field in a duct. Theory is developed to determine the bias and random errors in estimating the spectral density function for plane-wave propagation in the duct. A bivariate stochastic process has been employed to model the acoustic system. Experimental and theoretical calculations show that minimum-bias error can be achieved by using a small bandwidth in estimating the spectra and by locating the microphones close to the sample. Furthermore, random error can be minimized by maintaining a high coherence between microphone signals. This implies that the microphones should have a small spacing. However, high coherence may not be realized when a microphone location coincides with a node point in the sound field.