Performance of linear extrapolation methods for virtual sound field navigation

Performance errors are characterized for two representative linear extrapolation methods for virtual navigation of higher-order ambisonics sound fields. For such methods, navigation is theoretically restricted to within the so-called region of validity, which spherically extends from the recording ambisonics microphone to its nearest source, but the precise consequences of violating that restriction have not been previously established. To that end, the errors introduced by each method are objectively evaluated, in terms of metrics for sound level, spectral coloration, source localization, and diffuseness, through numerical simulations over a range of valid and invalid conditions. Under valid conditions, results show that the first method, based on translating along plane-waves, accurately reproduces both the level and localization of a source, whereas the second method, based on ambisonics translation coefficients, incurs significant errors in both level and spectral content that increase steadily with translation distance. Under invalid conditions, two common features of the performance of both methods are identified: significant localization errors are introduced and the reproduced level is too low. It is argued that these penalties are inherent to all methods that are bound by the region of validity restriction, including all linear extrapolation methods.