Characterization of a diffuse field in a reverberant room

Abstract

An efficient modal approach to characterize the diffuseness of the sound field in a rectangular room is presented. Using two simple descriptors, the correlation function and the spatial uniformity of the pressure field, a practical and convenient tool is proposed to study the diffuse field in the room. A precise criterion has been given in terms of the least permissible number of room modes to achieve an adequate diffusion. It has been shown that the criterion is in great accordance with the well-known “Schroeder frequency” limit for the diffuse field. Detailed calculations of the correlation function are presented to show the importance of the Δk/k correction terms to the well-known sin(kR)/kR prediction. A new closed form for the correlation function is thus derived. A discussion about the importance of having more than one descriptors is also presented. It is shown that a diffuse field can be established in a room with strong modal behavior under certain assumptions.

The coherence of reverberant sound fields

“…͑If the bandwidth is wider a correction described in Ref. 13 can be applied.͒ Conversely, at a given fixed time the corresponding spatial correlation functions equal the expressions given by Eqs. ͑1͒, ͑2͒, ͑3͒, and ͑4͒ with ϭ0.…”

“…1 Since then, many authors have studied pressure correlation functions in diffuse fields, experimentally [2][3][4][5][6][7][8] and theoretically. 3,[6][7][8][9][10][11][12][13] Spatial correlation functions of other quantities than the sound pressure in a diffuse sound field were derived more than 20 years ago, 10,12 but have never been verified experimentally, although they have found application in various areas, e.g., in active noise control 14,15 and in prediction of the response of a plate to excitation by a diffuse sound field. 16 The purpose of this paper is ͑i͒ to discuss the concept of a diffuse sound field, ͑ii͒ to present a new, efficient method of determining spatial correlation functions in a room, ͑iii͒ to present experimental results that validate the theoretical predictions in a real room, and ͑iv͒ to discuss possible applications.…”

Enhanced diffuse field model for ad hoc microphone array calibration

“…In our particular case of using broadband signal, all bands that have more than 25 modes generate a diffuse field [20]. Our empirical evaluations show that at least 5 diffuse field bands below the second zero crossing frequency are necessary to achieve reasonable accuracy in distance estimation.…”

“…If η( f ) ≥ 3 1 , there are enough excited modes to generate a diffuse field in the room [20], hence the critical frequency to achieve diffuseness is obtained as…”

Finite Element Sound Field Analysis of Diffuseness in Reverberation Rooms

“…In these studies, various descriptors were applied: sound intensity (Hanyu et al, 1995;Ikeda et al, 1996), modal density (Samejima et al, 1998), the coherence function (Jacobsen and Roisin, 2000), and so on. Brief reviews of descriptors are presented by Nelisse and Nicolas (1997) and by Jacobsen and Roisin (2000). Cook et al (1955) derived the spatial correlation function of a perfectly diffuse sound field and showed good agreement between the function and spatial correlation values of sound fields in actual reverberation rooms for high-frequency.…”