1940 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 21, NO. 9, SEPTEMBER 2013 Room Impulse Response Synthesis and Validation Using a Hybrid Acoustic Model Alex Southern, Samuel Siltanen, Damian T. Murphy, and Lauri Savioja, Senior Member, IEEE Abstract—Synthesizing the room impulse response (RIR) of an arbitrary enclosure may be performed using a number of alterna- tive acoustic modeling methods, each with their own particular ad- vantages and limitations. This article is concerned with obtaining a hybrid RIR derived from both wave and geometric-acoustics based methods, optimized for use across different regions of time or fre- quency. Consideration is given to how such RIRs can be matched across modeling domains in terms of both amplitude and boundary behavior and the approach is verified using a number of standard- ised case studies. Index Terms—FDTD, image-source, auralization, hybrid acoustic modeling. I. INTRODUCTION P REDICTING wave propagation behavior within an arbi- trary enclosure is beneficial in many areas of science. The simulation of sound wave propagation is particularly important as part of the architectural design process without which it is not possible to audition the acoustic qualities of a building before it has been constructed. Acoustic modeling techniques therefore provide an early indication of the objective acoustic properties of non-existent spaces through the analysis of the synthesized room impulse response (RIR) and subsequent derivation of stan- dard acoustical parameters [1], [2]. Such methods can then also be extended with some confidence to other virtual reality type applications, as found in first person gaming environments [3], [45], or in the reconstruction of historic buildings that no longer exist, or exist only in part [4]. Fig. 1 is an overview of the typical acoustic design and eval- uation workflow for a given environment that supports the anal- ysis of established objective metrics with subjective analysis based on critical listening. In this situation the designer is pre- sented with a rendered soundfield derived directly from the syn- thesized RIRs. Hence, the RIR synthesis and spatial encoding stage combined with the subsequent representation in a format suitable for audible rendering, result in an auralization of the Manuscript received August 21, 2012; revised December 19, 2012, April 16, 2013; accepted April 18, 2013. Date of publication May 14, 2013; date of current version July 12, 2013. This work was supported in part by the Academy of Finland under Project No. 138780 and in part by EPSRC Grant EP/J000108/1. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Woon-Seng Gan. A. Southern, S. Siltanen, and L. Savioja are with the Department of Media Technology, Aalto University School of Science, 02150 Espoo, Finland (e-mail: mrapsouthern@gmail.com; saasilta@tml.hut.fi; lauri.savioja@aalto.fi). D. T. Murphy is with the AudioLab, Department of Electronics, University of York, North Yorkshire YO10 5DD, U.K. (e-mail: dtm3@ohm.york.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASL.2013.2263139 Fig. 1. An overview of a typical acoustic design and evaluation workflow for a given environment based on the analysis of both objective measures obtained from RIR synthesis, and subjective listening via auralization. modeled enclosed space. In this context auralization allows the listener to experience auditory cues that would occur if the lis- tener was present in the equivalent real-world listening environ- ment. However in practice the auditory cues are only represen- tative of the listening situation rather than being absolutely iden- tical. Realizing this subjectively informed method of design, particularly with respect to concert hall acoustics, is the over- arching concept that motivates the contributions of this article. Currently established and accepted methods of predicting room acoustic characteristics are based on a geometric-based model of ray-like sound propagation. This approach is valid when representing wavelengths that are small in comparison to the dimensions of the bounding enclosure and internal objects. The main difference between these methods is in the discovery or approximation of reflection paths [5]. Each geometric method has its associated strengths and limitations although generally all rays that intersect a chosen listening region are recorded in a list for their energy, path length/time-of-arrival and angle-of-arrival, providing sufficient information to build a reflection echogram. At larger wavelengths the ray-like as- sumption no longer holds and this leads to a misrepresentation of the low frequency response of the acoustic model [6]. An alternative modeling approach is offered through wave- based methods that have been shown to be more appropriate in the low frequency range, e.g., [7]–[9]. These methods are based on a discrete numerical solution to the wave equation and are therefore a proper treatment of physical wave motion. How- ever, they are computationally intensive, especially when mod- eling large volumes and/or a wide frequency bandwidth such as the range of hearing. This is due to the large number of el- ements/calculations required to approximate continuous wave propagation with sufficient accuracy using a discrete system. Most previous research in attempting to develop a complete and accurate solution to synthesizing a RIR have been based 1558-7916/$31.00 © 2013 IEEE