Partitioned convolution algorithms for real-time auralization
Berlin / Logos-Verl. (2015, 2015) [Book, Dissertation / PhD Thesis]
Page(s): IV, 258 S. : Ill., graph. Darst.
Virtual Reality (VR) aims at the creation of responsive simulations, that provide humans the illusion of a world or environment, they can interact with. Therefore, the user is stimulated with sensory cues that are computer-generated, based on a model of a virtual world (scene). Considering the sense of hearing, the acoustic description of the scene is transformed into auditory stimuli, which are then provided using headphones or loudspeakers.Signal processing is fundamental to this process, called auralization. It involves digital filtering in several uses and in diverse forms (e.g. non-linear and linear filtering, time-invariant and time-varying filtering). A common requirement for VR is a low latency (immediate system response). The computational extent however, ranges from moderate to highly complex, depending on the application.This work focuses on finite impulse response filters (FIR filters), which are applied in binaural synthesis, spatial sound reproduction and artificial reverberation. Straightforward FIR filtering in the time-domain fails to satisfy the requirements stated above. These are met by implementing the FIR filtering using efficient mathematical algorithms for fast convolution. Since the 1960s different algorithmic concepts have been developed, often from the divide-and-conquer paradigm. The most popular example is fast convolution using the fast Fourier transform (FFT), which established as the standard tool. However, also fast convolution algorithms must be adapted to serve for real-time filtering. The most powerful concept hereby is partitioned convolution, which first splits the operands and then solves the partial problems using a fast convolution technique. Essential is that the decomposition conforms with real-time processing. This thesis considers three different classes of partitioned convolution algorithms for the use in real-time auralization: uniformly and non-uniformly partitioned filters, as well as unpartitioned filters. The algorithmic properties of each class are derived and guidelines for an optimal choice of parameters are provided. All techniques are analyzed regarding multi-channel processing, networks of filters and time-varying filtering, as needed in Virtual Reality. The work identifies suitable convolution techniques for different applications, ranging from resource-aware auralization on mobile devices to extensive room acoustical auralization on dedicated multi-processor systems.