Modeling the Impulse Response of an Office Room

i Abstract Repetition of signals due to reflection from ceiling, wall, floor and other objects in an enclosed environment can be perceived as the acoustic echo. It is resulted from the hands-free operation on the cellular, teleconferencing application and hearing aid system. Since the echo propagates in an enclosed environment, e.g. a room, the room acoustics acts as a filter. To remove the acoustic echo successfully, an estimate of the room impulse response is needed. Given experimental data, a system identification technique is employed as a tool to build the estimated model of the room impulse response. Herein, its model parameters can be estimated by means of an off-line or batch method in the least squares sense. Several traditional linear model structures have been presented. However, they often lead to an approximation of very high order. In order to reduce the number of estimated parameters, alternative methods for modeling the room impulse response need to be investigated. Approximation of the room impulse response by means of the so-called Laguerre and Kautz functions, which are the z-transform of a class of orthonormal exponentials, is then studied and examined. One of the most important parameters of these two functions is their dominating pole location. It can be shown that the number of estimated parameters is substantially reduced and the numerical accuracy is improved when the dominating pole is chosen properly. For a fixed model order, there exists the optimum choice of a dominating pole which gives the best approximation. Many methods to find a dominating pole are also given. Furthermore, since the typical echo response can be decomposed into two parts, i.e. the first part has rapid time variation and the second part is slowly decaying towards zero, the use of a two-stage echo canceller is then noteworthy to introduce and analyze. As a preliminary step to investigate the possibility of reducing the number of estimated parameters by the proposed models, we shall therefore not consider the on-line (recursive or adaptive) method to find the values of the model parameters. Instead, the data used in this thesis project has been collected from the system (echo path) that is made as near stationary as possible in order to be able to use the off-line method to estimate the model parameters.