Signal Processing Criteria and Statistical Error Analysis for Acoustic Measurements in Duct Systems

Abstract

A one-dimensional acoustic theory for random sound fields is presented. The theory is applied to the description of a random sound field in a tube of finite length terminated at the source and passive ends by arbitrary acoustical impedances. The theory is used to illustrate the spatial and spectral features of the acoustic field. These features are in many respects analogous to the well-known characteristics of a pure-tone sound field in a duct. However, the formulation in terms of a random sound field permits a more general investigation of measurement error than is possible using the pure-tone analysis. For example, it is shown that the familiar standing wave measurement problem is complicated by the presence of bias errors introduced by signal processing requirements.