Archontis Politis, 2015

Department of Signal Processing and Acoustics, Aalto University, Finland

[email protected]

This Matlab/Octave library was developed during my doctoral research in the [Communication Acoustics Research Group] (http://spa.aalto.fi/en/research/research_groups/communication_acoustics/), Aalto University, Finland. If you would like to reference the code, you can refer to my dissertation published here:

Archontis Politis, Microphone array processing for parametric spatial audio techniques, 2016
Doctoral Dissertation, Department of Signal Processing and Acoustics, Aalto University, Finland

This is a compact Matlab/Octave library implementing most common operations associated with higher-order ambisonics (HOA), which refer to a set of spatial audio techniques for capturing, manipulating and reproducing sound scenes, based on a spherical Fourier expansion of the sound field.

Most of the functionality of the library is demonstrated in the included script TEST_AMBI_SCRIPT.m. The same documentation can be also found in

[http://research.spa.aalto.fi/projects/ambi-lib/ambi.html]

The included functions implement HOA encoding of directional sounds, decoding using various decoding approaches, and rotation of HOA sound scenes. All operations are defined in terms of orthonormalized real Spherical Harmonics (N3D in ambisonic slang) and channel indexing according to $q = n^2+n+m+1$, where n is the order and m is the degree (ACN in ambisonic slang). However, functions are included to convert to and from N3D/ACN to some other established conventions (namely semi-normalized SHs (SN3D) and an alternative channel indexing, termed SID).

Ambisonic decoding can be approached from various sides, more physically inspired or more perceptually inspired. Five approaches are implemented

• 1. Sampling or projection decoding (transpose)
• 2. Mode-matching decoding (pseudo-inverse)
• 3. Energy-preserving decoding [ref.1]
• 4. All-round ambisonic decoding [ref.2]
• 5. Constant-angular spread decoding [ref.3]

Apart from the two first traditional approaches, the three last are more recent and more perceptually motivated. They are also more flexible and robust, in terms of loudspeaker layouts.

Additionally, a function evaluating and visualizing the popular ambisonic performance measures, velocity and energy vectors, along with overall energy and amplitude preservation, is included.

Max-rE weighting for the decoder [ref.4 & ref.2] can be optionally enabled.

ALLRAD and CSAD decoders require computation of amplitude and energy panning gains, and large spherical uniform sampling schemes (t-Designs). Both of these can be found firs in the Matlab/Octave VBAP library in

[https://github.com/polarch/Vector-Base-Amplitude-Panning]

and the general Spherical harmonic transform library by the author found in

[https://github.com/polarch/Spherical-Harmonic-Transform],

These two libraries should be added to the Matlab path before executing this script.

Rotation, apart from the case of simple B-format, also depends on the larger spherical harmonic transform library, which contains many other operations that may be of interest to ambisonics, like directional smoothing (spherical convolution) and directional weighting/shaping (spherical multiplication).

The library contains the following main functions:

• ambiDecoder: Compute a HOA decoding matrix for a specified order and a specified method, with or without max-rE weighting
• analyzeDecoder: Analyze amplitude, energy, velocity and energy vector magnitudes and directional errors and spread, for an ambisonic decoder, or from panning gains
• getRSH: returns values of real orthonormal spherical harmonics vectors of directions
• encodeHOA_N3D: encode a number of source signals from various directions to arbitrary-order HOA signals (N3D, ACN)
• encodeBformat: encode a number of source signals from various directions to traditional B-format signals
• decodeHOA_N3D: decode HOA signals to a loudspeaker setup, using a certain decoding matrix (frequency-dependent decoding possible, see below)
• decodeBformat: decode B-format signals to a loudspeaker setup, using a certain decoding matrix
• rotateHOA_N3D: rotate sound scenes encoded or recorded in HOA signals, using a yaw-pitch-roll convention
• rotateBformat: rotate sound scenes encoded or recorded to B-format signals, using a yaw-pitch-roll convention
• allrad: implements the all-round ambisonic decoder
• csad: implements the constant-angular spread decoder
• getLayoutAmbisonicOrder: Compute the equivalent ambisonic order for regular and irregular speaker arrangements
• getMaxREweights: Compute the max-rE weights for a certain order, for decoding (or encoding) weighting
• getTheoreticalEVmag: Compute the theoretical energy vector magnitude of a plane-wave encoded to a certain order, with max-rE weighting
• plotSphericalGrid: Plots angular quantities in a 2D azimuth-elevation grid, with loudspeaker positions superimposed
• convert_ACN_SID: Convert HOA signals with the ACN indexing to HOA signals with the SID indexing, and back
• convert_N3D_SN3D: Convert HOA signals with the N3D normalization to HOA signals with the SN3D normalization, and back
• convert_N3D_Bformat: Convert 1st-order signals with the N3D and ACN conventions to traditional B-format, and back

For any questions, comments, corrections, or general feedback, please contact [email protected]

[1] Zotter, F., Pomberger, H., Noisternig, M. (2012). 
Energy-Preserving Ambisonic Decoding. Acta Acustica United with Acustica, 98(1), 37:47.

[2] Zotter, F., Frank, M. (2012). 
All-Round Ambisonic Panning and Decoding. Journal of the Audio Engineering Society, 60(10), 807:820.

[3] Epain, N., Jin, C. T., Zotter, F. (2014). 
Ambisonic Decoding With Constant Angular Spread. Acta Acustica United with Acustica, 100, 928:936.

[4] Daniel, J. (2001). 
Representation de champs acoustiques, application ? la transmission et ? la reproduction de scenes sonores complexes dans un contexte multim?dia. Doctoral Thesis. Universite Paris 6.

[5] Makita, Y. (1962). 
On the directional localization of sound in the stereophonic sound field. EBU Review, 73, 1536:1539.

[6] Gerzon, M. A. (1992). 
General Metatheory of Auditory Localization. In 92nd AES Convention (Preprint 3306). Vienna, Austria.

[7] Merimaa, J. (2007). 
Energetic sound field analysis of stereo and multichannel loudspeaker reproduction. In 123rd AES Convention. New York, NY.

[8] Matthias, F. (2013). 
Phantom Sources using Multiple Loudspeakers in the Horizontal Plane. Doctoral thesis, Institute of Electronic Music and Acoustics, University of Music and Performing Arts, Graz

[9] Laitinen, M., Vilkamo, J., Jussila, K., Politis, A., & Pulkki, V. (2014). 
Gain normalization in amplitude panning as a function of frequency and room reverberance. In 55th International Conference of AES. Helsinki, Finland.

[10] Frank, M. (2013). 
Source Width of Frontal Phantom Sources: Perception, Measurement, and Modeling. Archives of Acoustics. 38(3), 311?319

[11] Daniel, J. (2003). 
Spatial Sound Encoding Including Near Field Effect : Introducing Distance Coding Filters and a Viable , New Ambisonic Format. In 23rd International Conference of AES. Copenhagen, Denmark.