Binaural displays for immersive listening must model realistic acoustic environments, multiple sound sources, and accommodate source and head motion. Many displays accomplish this by convolving collections of spatially distributed point sources with head-related transfer functions (HRTFs). The computational load of such a system scales linearly with the number of HRTFs modeled by the display. Realistic scenes often require a large number of HRTFs, and this framework is computationally burdensome. We propose a method that significantly eases this load by formulating the HRTF filter array as a state-space system. Three state-space architectures are explored. The performance of the most general architecture is found to suffer due to the interaural time delay (ITD). This problem may be circumvented with two alternative architectures, although the ideal choice depends on the specific display application. For each architecture, two order-reduction techniques are explored. Both techniques are based on the Hankel operator; one is ad hoc and simple to implement whereas the other is optimal in the Hankel norm. The two methods yield similar auditory performance, although the optimal method may be desirable for HRTF approximation.

Binaural displays for immersive listening must model reverberant acoustic environments, multiple sound sources, and compensate for head motion. Many displays accomplish this by convolving collections of spatially distributed sources with head-related transfer functions (HRTFs). In the absence of reflections, the computational load scales linearly with the number of sources; however, when reflections are present, the load scales exponentially such that the binaural display reaches the limit of available processing power for even relatively sparse acoustic scenes. We propose a method that significantly eases this exponential growth by formulating the HRTF filter array as a MIMO state-space system. Two MIMO architectures are explored; the relative merits of each are found to depend on the specific application. Hankel-optimal methods are found to be a good choice for model reduction, and yield displays with superior approximation quality relative to conventional FIR filter arrays of equal computational complexity.

Much research in music information retrieval has focused on query-by-humming systems, which search melodic databases using sung queries. The database retrieval aspect of such systems has received considerable attention, but query processing and the melodic representation have not been examined as carefully. Common methods for query processing are based on musical intuition and historical momentum rather than specific performance criteria; existing systems often employ rudimentary note segmentation or coarse quantization of note estimates. In this work, we examine several alternative query processing methods as well as quantized melodic representations. One common difficulty with designing query-by-humming systems is the coupling between system components. We address this issue by measuring the performance of the query processing system both in isolation and coupled with a retrieval system. We first measure the segmentation performance of several note estimators. We then compute the retrieval accuracy of an experimental query-by-humming system that uses the various note estimators along with varying degrees of pitch and duration quantization. The results show that more advanced query processing can improve both segmentation performance and retrieval performance, although the best segmentation performance does not necessarily yield the best retrieval performance. Further, coarsely quantizing the melodic representation generally degrades retrieval accuracy.