Acoustic Room Impulse Response Shaping
Impulse response shaping is a technique for modifying the characteristics of a linear channel to achieve desirable characteristics. The technique is well-known in the field of wireless communication. Acoustic impulse response shaping is used to reduce the effects of reverberation on audio signals propagating inside a room and is thus used for listening room compensation. This thesis addresses innovative approaches for acoustic impulse response shaping. Many techniques have been proposed in the literature for canceling or reducing the effect of reverberation on the audio signal. Impulse response inversion attempts to completely cancel the effect of reverberations whereas impulse response shortening (or shaping) only partly equalizes the room impulse responses. Shortening has less stringent constraints than inversion and this can result in more robust solutions and thus more practically realizable systems. Acoustic impulse response shaping works on measured room impulse responses and designs pre-filters to be placed before the loudspeakers so that the reverberation is reduced at the listening positions. When sampled, the room responses typically contain thousands or tens of thousands (N ) of samples. Thus, the shaping algorithm needs to be computationally fast and memory efficient in order to implement the system in real time. The techniques presented in the literature use interior point methods or steepest descent algorithms, which are computationally slow or require memory of the order of N² . This thesis presents shaping approaches based on the Dual Augmented Lagrangian Method (DALM), known in the literature on sparse reconstruction for its super-linear convergence. The method presented here also makes use of the concept of a Forward Adjoint Oracle (FAO) to make the shaping algorithm memory efficient. Thus, the thesis presents computationally fast and memory efficient shaping algorithms that can be used for practically realizable systems. The thesis also presents robust shaping approaches. The measured room responses may contain measurement errors or noise and can vary from time to time. These variations may be due to changes in atmospheric conditions (such as temperature or humidity) or due to change in position of objects inside a room. While design approaches over multiple microphone positions have been proposed for design of filters that are robust to change in microphone positions, a more rigorous approach is statistical, involving the inclusion of some statistical constraints into the optimization problem. The thesis presents both the approaches viz., a computationally faster version (using DALM) of the already proposed design over multiple positions and a statistically robust shaping formulation. The latter limits the probability of large errors between expected and obtained response to be less than a specified value. This ensures that the solution is robust to variations in the room response. The shaping algorithm works in the time domain, shaping the temporal characteristics of the room response to a desired form. The frequency response of the shaped response can contain potentially undesirable peaks and troughs. This thesis therefore presents an approach for an efficient projection to improve spectral flatness of the resultant response. This algorithm can be combined with the fast and memory efficient DALM based approach to achieve joint time and frequency shaping. Finally, the thesis also presents a computationally fast algorithm based on DALM for pressure matching used in sound field reproduction. Impulse response shaping is applied in sound field reproduction, showing that the levels of pre-reverberation induced by a temperature change can be reduced. This application is different from impulse response shaping approaches presented in the previous chapters and highlights the flexibility of the algorithm developed in this thesis and its wide range of applications.