Spectral Impairment for Two-Dimensional Higher Order Ambisonics

The representation of sound fields by spherical or cylindrical harmonics, also known as higher order Ambisonics (HOA), is a flexible format where the accuracy of the representation depends on the order N. It is shown that reproducing 2D HOA with uniformly distributed loudspeakers on a circle radiating plane waves in a nonreverberant environment will lead to spectral impairment if the number of loudspeakers M is higher than 2N + 1. The impairments vary with both the angle, that is, the angular difference between source and receiver relative to the center of the circle, and the product kr, where k is the wavenumber and r the distance from the center of the circle. It is therefore not possible to correct the impairments with a filter for multiple radii. For classical first-order Ambisonics the near perfect reconstruction area is so small that it must be regarded solely as a sweet-spot technique and filtering should be considered when using more than three loudspeakers. Furthermore, for HOA the number of loudspeakers is a tradeoff between the reproduction error for kr N.

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