Higher-Order Ambisonic (HOA) Encoder — User Guide

Spatial audio encoding: converts mono source into ambisonic B-format with 1st, 2nd, or 3rd order spherical harmonic decomposition. Supports 3D positioning (azimuth, elevation, distance) with visualization and distance attenuation.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel

What this does

This script encodes a mono sound source into ambisonic B-format — a full-sphere surround sound format based on spherical harmonics. Position source in 3D space (azimuth 0-360°, elevation -90° to +90°, distance in meters), choose ambisonic order (1st=4 channels, 2nd=9 channels, 3rd=16 channels), and script generates individual ambisonic channels (W, X, Y, Z...) with spherical harmonic weighting. Includes distance attenuation and top-down visualization. Output requires ambisonic decoder for playback on speakers or headphones.

Ambisonic coordinate system (top view): Front (0°) | N | Left ------+------ Right (270°) | (90°) S | Back (180°) Elevation: -90° (below) to +90° (above) Distance: Meters from origin (listener position)

Quick start

Select one Sound object in Praat (mono or stereo — will convert to mono).
Run script… → Load HOA Encoder script.
Choose Position_preset (10 presets) or select "Custom" for manual positioning.
If Custom: Set Azimuth (0-360°), Elevation (-90 to 90°), Distance (meters).
Set Reference_distance (1.0m default) for distance attenuation calculation.
Choose Ambisonic_order: 1st (4ch), 2nd (9ch), or 3rd (16ch).
Enable Normalize_output and Show_visualization.
Click OK — encoding instant, individual channels appear in Objects list, visualization in Picture window.

Quick tip: Start with Front center preset and 1st order to understand basics. Enable visualization to see source position graphically. Output channels (W, X, Y, Z...) appear as separate Sound objects — use ambisonic decoder to render to speakers.

Ambisonic Theory

What are Ambisonics?

Spatial audio format based on spherical harmonics:

Full-sphere surround: Captures 3D sound field (horizontal + vertical)
Scene-based: Independent of playback speaker arrangement
Scalable resolution: Higher orders = better spatial precision
Decoder-based playback: Requires decoder to render to specific speaker setup

Ambisonic Orders

Order	Channels	Resolution	Use Case
1st order	4 (W,X,Y,Z)	Low spatial resolution	Basic 3D audio, mobile, VR
2nd order	9	Medium resolution	Better localization, planetariums
3rd order	16	High resolution	Professional spatial audio, cinema

Channel count formula: (order + 1)² channels

1st: (1+1)² = 4 channels
2nd: (2+1)² = 9 channels
3rd: (3+1)² = 16 channels

Coordinate System

Azimuth (Horizontal Angle)

Azimuth: 0° to 360° (horizontal plane) 0° = Front (straight ahead) 90° = Right 180° = Back (behind) 270° = Left 360° = Front (same as 0°) Mathematical convention: Measured clockwise from front when viewed from above

Elevation (Vertical Angle)

Elevation: -90° to +90° (vertical plane) +90° = Directly above (zenith) 0° = Horizontal plane (same height as listener) -90° = Directly below (nadir) Most common: 0° (horizontal plane sources)

Distance (Radial)

Distance: Meters from origin (listener position) Distance attenuation formula: gain = reference_distance / distance Example: distance=2m, reference=1m gain = 1/2 = 0.5 (-6 dB) Example: distance=0.5m, reference=1m gain = 1/0.5 = 2.0 (+6 dB) Inverse distance law: Sound pressure decreases with distance

Position Presets

Preset	Azimuth	Elevation	Distance	Description
Front center	0°	0°	1.5m	Straight ahead, close
Front left	315°	0°	2m	45° left of center
Left	270°	0°	2m	Directly left
Rear left	225°	0°	3m	45° behind, left
Rear center	180°	0°	3m	Directly behind
Rear right	135°	0°	3m	45° behind, right
Right	90°	0°	2m	Directly right
Front right	45°	0°	2m	45° right of center
Above	0°	+90°	2.5m	Directly overhead
Below	0°	-90°	2.5m	Directly underneath

Ambisonic Channels

1st Order (4 Channels)

Channel 0 (W): Omnidirectional (0th order) Formula: W = 1.0 Pressure component, equal in all directions Channel 1 (Y): Figure-8 left-right (1st order) Formula: Y = cos(el) × sin(az) Positive = right, negative = left Channel 2 (Z): Figure-8 up-down (1st order) Formula: Z = sin(el) Positive = up, negative = down Channel 3 (X): Figure-8 front-back (1st order) Formula: X = cos(el) × cos(az) Positive = front, negative = back

2nd Order (5 Additional Channels)

Adds channels V, T, R, S, U (channels 4-8)

Higher spatial resolution
Better localization accuracy
More complex spherical harmonic functions

3rd Order (7 Additional Channels)

Adds channels Q, O, M, K, L, N, P (channels 9-15)

Professional-grade spatial resolution
Precise source localization
Complex spherical harmonic decomposition

Parameters

Parameter	Type	Default	Description
Position_preset	choice	Custom	10 position presets or manual
Azimuth	real	0°	Horizontal angle (0-360°)
Elevation	real	0°	Vertical angle (-90° to +90°)
Distance	real	1.0m	Radial distance from origin
Reference_distance	real	1.0m	Distance for 0 dB attenuation
Ambisonic_order	choice	1st order	Spatial resolution (1st/2nd/3rd)
Normalize_output	boolean	yes	Scale all channels to 0.99 peak
Show_visualization	boolean	yes	Draw top-down position diagram

Output

Individual channel objects in Objects list:

1st order: W, X, Y, Z (4 Sound objects)
2nd order: + V, T, R, S, U (9 total)
3rd order: + Q, O, M, K, L, N, P (16 total)

Info window displays:

Input sound info (mono conversion if needed)
Distance attenuation calculation (gain in linear and dB)
Channel encoding values
Final position summary

Picture window (if visualization enabled):

Top-down circular diagram (4m radius)
Concentric distance circles (1m, 2m, 3m, 4m)
Cardinal direction labels (Front, Back, Left, Right)
Red arrow showing source position and distance
Position text (azimuth, elevation, distance)

Important: Output channels are B-format ambisonic signals, not playable audio. Requires ambisonic decoder to render to speakers or headphones. Use specialized ambisonic tools/plugins for playback (IEM Plug-in Suite, Ambix, Reaper ReaPlugs, etc.).

Typical Workflow

Step-by-step ambisonic production:

Encode sources: Run script for each mono source at different positions
Mix channels: Combine corresponding ambisonic channels (all W, all X, etc.)
Export B-format: Create multi-channel file with channel order (W,X,Y,Z...)
Decode: Use ambisonic decoder for target speaker configuration
Playback: Render to specific setup (stereo, 5.1, binaural, dome, etc.)

Channel mixing example: Two sources (A at front, B at left)

Mix: A_W + B_W → combined W channel
Mix: A_X + B_X → combined X channel
Mix: A_Y + B_Y → combined Y channel
Mix: A_Z + B_Z → combined Z channel
Result: Single 4-channel B-format with both sources

Applications

Immersive audio production:

Virtual reality (VR) soundscapes
360° video audio
Planetarium shows
Immersive installations

Spatial composition:

Acousmatic music with spatial trajectories
Multi-speaker dome performances
Experimental spatial audio art

Research:

Psychoacoustic spatial perception studies
3D audio algorithm testing
Spatial hearing experiments

Post-production:

Film surround sound (beyond 5.1/7.1)
Game audio (dynamic 3D positioning)
Broadcast spatial audio

Technical Notes

Spherical Harmonic Functions

Ambisonic encoding uses orthogonal spherical harmonics:

Mathematical basis: Spherical Harmonics Y_l^m(θ,φ)
Order (l): 1, 2, 3... determines spatial resolution
Degree (m): -l to +l determines directional pattern
Normalization: N3D (orthonormal) used in this script

Distance Attenuation

Inverse distance law: gain = reference_distance / distance Examples: distance=1m, ref=1m: gain=1.0 (0 dB) distance=2m, ref=1m: gain=0.5 (-6 dB) distance=4m, ref=1m: gain=0.25 (-12 dB) distance=0.5m, ref=1m: gain=2.0 (+6 dB) Each doubling of distance = -6 dB

Normalization Schemes

This script uses N3D (Schmidt semi-normalized):

Standard for modern ambisonics
Used by: IEM, Ambix, Facebook 360, YouTube spatial
Alternative: SN3D, FuMa (older formats)

Limitations

Mono input only: Stereo automatically converted to mono
Static positioning: No motion/trajectory support (encode multiple times for animation)
No near-field compensation: Distance affects amplitude only, not frequency
Decoder required: Cannot play B-format directly on standard speakers
No Doppler effect: Moving sources need external processing
Single source per run: Mix multiple encoded sources for complex scenes

Further Resources

Ambisonic decoders:

IEM Plug-in Suite (free, comprehensive)
Ambix (free, open-source)
Reaper ReaPlugs (free, includes ambisonic tools)
Blue Ripple Sound O3A (commercial)

Learning resources:

Ambisonics.net — Tutorial and specifications
York University Ambisonic Toolkit
IEM documentation and video tutorials