HRIR Order Reduction Using Approximate Factorization

A factorization technique is proposed which allows for a direction independent component to be extracted from a set of head related impulse responses (HRIRs). Each individual HRIR is split into a pair of filters, a direction independent component which is common to all HRIRs in the dataset and a direction dependent component which is particular to that HRIR. When these are convolved together, the result is a close approximation to the original HRIR. However, different initial conditions for the factorization algorithm can converge to solutions with drastically different pairs of direction independent and dependent components each of which offer a similarly low reconstruction error. That is, it appears the problem is one with multiple similar local minima. To address the issue of selection of a minimum with psychoacoustic significance the factorization is refined using a regularization technique. Two variants of the regularization are proposed to provide a more robust algorithm that should be less sensitive to the choice initial condition. One of these is suitable for minimum phase HRIR data and allows for very short direction-dependent components to be obtained. The other is suited to initial delay inclusive HRIR data and allows for this initial time delay to be maintained in the direction dependent components. These techniques are applied to HRIR data from the KEMAR and CIPIC databases and the results show low reconstruction error when the original and reconvolved HRIRs are compared. The results of subjective listening tests comparing the performance of factorized and unfactorized HRIRs with truncated HRIRs in an Ambisonic based virtual loudspeaker array are also presented. These suggest there is minimal perceptual difference between factorized and unfactorized HRIRs.