Acoustically Inspired Adaptive Algorithms for Modeling and Audio Enhancement via Orthonormal Basis Functions

Sahar Hashemgeloogerdi

Supervised by Professor Mark Bocko

Computer Studies Building, Room 426

Interactive acoustic systems such as spatial audio rendering, 3D sound localization, and feedback cancellation systems rely on real-time audio signal processing methods. The ability of systems to adapt quickly and provide lifelike acoustic experiences depends on computational efficiency and accuracy of the audio signal processing algorithms. Hence, accurate modeling of acoustic environments, e.g., room acoustics, head related transfer functions (HRTFs), and acoustic feedback paths, utilizing as few parameters as possible is essential for a wide variety of applications from virtual reality to healthcare.

In this dissertation, we developed an accurate yet computationally efficient modeling method to represent highly reverberant acoustic systems. By comparing to measured impulse responses, we showed that the proposed method significantly enhances the modeling accuracy compared to state-of- the-art methods. The method we developed relies on the time-frequency representation of an acoustic system, enabling accurate modeling in real-time using orthonormal basis functions over a wide range of subband frequencies. To realize subband decomposition, we introduced the utilization of the dual-tree complex wavelet transform, providing aliasing-free subbands. Furthermore, the proposed method is less sensitive to variations of the source and microphone locations since it incorporates common acoustical poles of the system. The common acoustical poles correspond to the resonant prop- ties of the system and do not change if the source and microphone locations change.

We developed two inherently stable least-squares algorithms for the precise estimation of the common acoustical poles from multichannel transfer functions measured with different source and microphone locations. In contrast to previous algorithms, which may have limited accuracy or other limitations imposed by nonlinear optimization, the proposed algorithms precisely estimate the common acoustical poles after a few iterations. We examined our algorithms using measured HRTFs and room transfer functions. Results show that the estimated common acoustical poles accurately match the resonance frequencies of the ear canal and precisely agree with the theoretical poles for room acoustic responses.