Magnitude-Least-Squares Binaural Ambisonic Rendering with Phase Continuation

Abstract

Binaural rendering of Ambisonic signals is one of the most accessible ways of experiencing spatial audio. However, due to technical constraints, the rendering algorithm needs special care and advanced signal processing, especially for low Ambisonic orders. Next to more intricate parametric model-based approaches, other computationally efficient algorithms have emerged that provide powerful options. One particularly effective technique is the idea to discard the phase of HRTFs above a certain frequency limit, where the auditory system is less sensitive to phase information and instead utilize the available low order resolution to achieve an optimized magnitude response. This technique is known as the magnitude-least-squares (magLS) binaural rendering algorithm and often implemented as a recursive solution over frequency bins. However, altering the phase can lead to group delay errors, and therefore, frequency dependent misalignment, i.e. dispersion, of the HRIR. This issue is particularly prevalent with measurements that show a significant pre-delay, such as linear phase HRTFs. Besides analyzing the phase behavior of magLS, we present an effective way to preserve the group delay by continuing the phase over frequency as observed in the lower frequency region unaffected by the phase modification. This simple modification leads to further improvements for the magLS binaural Ambisonics rendering.