Statistical considerations on stationary-random noise propagating through a solid medium

In this paper the noise propagation through a solid medium is considered to study how the parameters of the statistical model change. In particular the external and internal sound fields of a box are taken into account. It is experimentally shown that the variance of the real and the imaginary parts of the external stationary random noise change differently while going through the box walls. The generalized Rayleigh distribution is shown to be more suitable to model the noise inside the cavity instead of the classical Rayleigh distribution. Starting from this outcome it has been studied how this noise affects a signal. It is known that a signal modulus affected by stationary random noise can be described by using the Rice distribution if the real and imaginary parts of the noise are statistically independent and identically distributed with zero mean and equal variances. Otherwise the less popular generalized Rice distribution must be used. The main differences of using the Rice or the generalized Rice distributions are shown by considering phasors both with constant and variable phases. In this paper it is shown that the bias estimation depends on the phase of the phasor if the variances of the real and imaginary parts are different and a numerical quantification is given. The attained results are useful when performing measurements of the sound pressure field due to a sound source inside a cavity affected by external noise.