Angular Spectral Plane-Wave Expansion of Nonstationary Random Fields in Stochastic Mode-Stirred Reverberation Processes

TL;DR

This paper derives an explicit integral expression for the nonstationary random field inside a mode-stirred reverberation chamber, revealing how nonstationarity modulates spectral fields and incorporating initial field conditions.

Contribution

It introduces a closed-form oscillatory process expansion for nonstationary fields in reverberation chambers, including effects of initial conditions and specific second-order processes.

Findings

Explicit integral expression for nonstationary field expansion

Demonstration of spectral modulation due to nonstationarity

Extension to second-order processes relevant to device perception

Abstract

We derive an integral expression for the plane-wave expansion of the time-varying (nonstationary) random field inside a mode-stirred reverberation chamber. It is shown that this expansion is a so-called oscillatory process, whose kernel can be expressed explicitly in closed form. The effect of nonstationarity is a modulation of the spectral field on a time scale that is a function of the cavity relaxation time. It is also shown how the contribution by a nonzero initial value of the field can be incorporated into the expansion. The results are extended to a special class of second-order processes, relevant to the perception of a mode-stirred reverberation field by a device under test with a first-order (relaxation-type) frequency response.