Higher-Order Ambisonic Decoder — AmbiX to Loudspeaker Arrays

Decode 1st–5th-order Full-3D ambiX ACN/SN3D to horizontal or immersive loudspeaker layouts with automatic order detection and actual spherical-harmonic matrix-rank diagnostics.

Author: Shai CohenAffiliation: Department of Music, Bar-Ilan University, IsraelLicense: MIT LicenseRepo: Praat AudioTools

Contents:

What this does Automatic order detection Layouts Matrix rank Decode methods Workflow examples Interpretation

What this does

Higher-Order Ambisonic Decoder converts Full-3D ambiX B-format (ACN/SN3D) into loudspeaker feeds. It accepts orders 1–5 and provides horizontal, immersive, and cinema-style layouts including 7.1.4 and 22.2.

The decoder never asks the user to declare the HOA order. The order is inferred from the actual input component count, preventing a 4-channel HOA1 file from being accidentally treated as HOA5.

Automatic order detection

Input	Detected format
4 components	HOA1
9 components	HOA2
16 components	HOA3
25 components	HOA4
36 components	HOA5

Combined mode accepts one multichannel AmbiX Sound. Legacy mode accepts the same component counts as separately selected mono Sounds in ACN order.

Built-in loudspeaker layouts

Available targets include 2.0, triangle, quad, pentagon, hexagon, 5.0, 5.1, 7.0, 7.1, 8-ring, 12-ring, 16-ring, 7.1.4, and 22.2. LFE output slots are created as silence, because Ambisonics carries no directional LFE signal.

Auto full-rank policy: HOA1 → 7.1.4; HOA2 → 22.2; HOA3 → 22.2. HOA4 and HOA5 have no built-in full-rank target, so Auto stops rather than silently discarding component dimensions. You may still choose 22.2 manually and receive an explicit rank warning.

Actual spherical-harmonic matrix rank

The script evaluates the real spherical-harmonic sampling matrix for the exact loudspeaker geometry and reports its rank against the number of Ambisonic components.

HOA1 on 7.1.4 → rank 4 / 4 HOA2 on 22.2 → rank 9 / 9 HOA3 on 22.2 → rank 16 / 16 HOA4 on 22.2 → rank 20 / 25 HOA5 on 22.2 → rank 22 / 36

A full-rank result means the chosen directions span the component space. It does not mean that a simple projection decoder is perceptually optimal. Irregular arrays such as 7.1.4 and 22.2 are explicitly reported as approximate projection decodes.

Horizontal layouts and Full-3D input: a horizontal array cannot reproduce all vertical modes of Full-3D Ambisonics. The rank report exposes this directly instead of relying on speaker count alone.

Decode methods

Method	Behavior
Basic sampling / projection	Raw real-SH projection with per-order SN3D scaling.
Max-rE	Applies order-dependent Max-rE weights to reduce side-lobe energy and improve directional concentration.
In-phase	Applies in-phase order weights for a more conservative, phase-coherent spatial pattern.

Shared peak protection attenuates all speaker feeds together only if needed, preserving relative decode levels.

Workflow examples

Spatial Trajectory Painter → HOA3 / 16ch
                         ↓
                 Ambisonic Decoder
                  ↙              ↘
              7.1.4              22.2

Speaker Bed → HOA Encoder → ambiX master → HOA Decoder → new speaker array

Interpretation and limitations

Output channels are loudspeaker feeds, not Ambisonic components.
A 4-channel HOA1 input decoded to 7.1.4 correctly produces 12 output channels; this does not increase the Ambisonic order.
Manual HOA4/5 → 22.2 is allowed but explicitly rank-deficient.
The built-in decoder is a practical sampling/projection decoder, not AllRAD, EPAD, or a calibrated room decoder.
For headphone rendering, use the companion IRCAM AmbiX B-format → Binaural workflow.