Approximate convolution using partitioned truncated singular value decomposition filtering for binaural rendering

Abstract

In conventional binaural rendering a pair of head-related impulse responses (HRIR), measured from source direction to left and right ears, is convolved with a source signal to create the impression of a virtual 3D sound source when played on headphones. It is well known that using HRIRs measured in a real room, which includes a natural reverberant decay, increases the externalization and realism of the simulation. However, the HRIR filter length in even a small room can be many thousands of taps leading to computational complexity issues in real world implementations. We propose a new method, partitioned truncated singular value decomposition (PTSVD) filtering, for approximating the convolution by partitioning the HRIR filters in time, performing a singular value decomposition on the matrix of filter partitions, and choosing the M singular-vectors corresponding to the M largest singular values to reconstruct the HRIR filters. We will show how this can be implemented in an efficient filter-bank type structure with M tapped delay lines for real-time application. We also show how improvements to the method, such as modeling the direct path HRIR separately can lead to improved rendering at minimal computational load. © 2013 Acoustical Society of America.