Ambisonic Studio
Fifth Order Planar B-Format Encoding and Decoding

August 2019 • Important note

The information on this page is now obsolete.

For high order ambisonic (HOA) production, we recommend using the following DAW and VST plug-ins:

Cockos Reaper | Aalto University SPARTA and COMPASS plug-ins | IEM Plug-in Suite | Matthias Kronlachner's ambiX plug-ins | Blue Ripple Sound's O3A Core suite

We recommend the following book as the reference on Ambisonics audio production, including up to date information about high order Ambisonics:

Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality

Highslide JSExperimental Spherical Microphone
Image: Angelo Farina

Highslide JSMH Acoustics em32 Eigenmike


Higher Order Ambisonic

The most common form of Ambisonic B-Format is of the "first order" type. The famous WXYZ channels were present from the start, whether coming out of a SoundField microphone or, a few years later, synthesized by hardware analog encoders/panners. But even in his seminal 1973 paper, Periphony: With-Height Sound Reproduction, Michael Gerzon paved the way for Higher Order Ambisonic (HOA). Although the terminology and nomenclature has evolved, the concept of HOA was completely described. The idea of a hierarchical surround sound system, where the spatial information is always complete, but where you gain spatial resolution by adding channels is still revolutionary today, in the sense that it's not in use or even only generally understood.

On the microphone side, Gerzon was already in 1973 beyond the first order SoundField (that would be released four years later) by suggesting a HOA SoundField-like microphone with 12 capsules for producing the complete nine channel set of second order B-Format. As far as we know, a dodecahedron of first order cardioids for generating second order B-Format has never seen the light of day. But recent research and development in solid spherical array with omnidirectional capsules should come to fruition in a commercial product with the Eigenmike. This microphone, even without a mentioned filiation to Ambisonic, is clearly in the spirit of it with the synthesis of virtual microphones using spherical harmonic components. HOA, though, is not limited to eventual higher order microphone arrays.

While Ambisonic analog hardware of the early 80’s for the encoding and processing of mono and stereo source material were limited to first order B-Format, the advent of Ambisonic digital signal processing, which could be symbolized by the processing unit of the 1993 AGM Digital MR1 SoundField-like microphone system, ushered the new era of HOA. Since then, HOA DSP has made entries in the field of traditional timeline-based production systems – Digital Audio Workstations – but also in productions featuring interactive environments.

That being said, Ambisonic Studio is interested in developing HOA software tools for DAWs, namely Steinberg Nuendo. Why Nuendo? Although it is true that, compared to Apple Logic Pro 8 (that has redefined the price point for a professional DAW), Nuendo is shamefully expensive, it still has the most flexible mutichannel internal structure that can be used in many “standard” and not-so standard ways.


Highslide JSAmbisonic B-Format, up to the 3rd order.

HOA Planar Encoding


Encoding to Fifth Order Planar B-Format

A complete fifth order B-Format signal has a total of 36 channels. Not necessarily an impossible task for today’s fast computers, it represents however a challenge to implement with audio production software not designed around B-Format. Nuendo multichannel structure can support up to 12 channels: with HOA, it’s an important limiting factor, but these 12 channels are nonetheless more than what most competing DAWs offer. These 12 channels can accommodate a complete set of second order B-Format (nine channels) or various combinations of 3D/2D B-Formats. Since most of the surround sound productions done in DAWs are destined for film and video, where vertical surround information is not exploited, we decided to utilize the 12 channels to maximize the horizontal resolution. We're also keeping one order of vertical information to be directly compatible with common 3D first order source material out of SoundField and other tetrahedral arrays.

Our 12 channels are then W X Y Z U V P Q 4C 4S 5C 5S. The “4C” and up nomenclature is our own and becomes self-evident when one looks at the B-Format encodings. They follow usual B-Format encodings.

We have made so far a mono source dynamic panner, the Solo2B5, a stereo source dynamic panner, the Duo2B5, and 5.1 source encoder, the Five2B5. The panners can be coupled to the B2B5, a processing unit for rotation and axis flipping.


Highslide JSHigh Order Cardioids

Highslide JSHigh order planar B-Format pentagonal decoding


Decoding Fifth Order Planar B-Format: A Continuum of Virtual Cardioid Microphones

Historically, 1st order B-Format decoders featured user configurable options to psychoacoustically optimize the decoding. One of this feature is a pre-decode shelf-filtering of the signal by boosting the XYZ channels and lowering the W channel at frequencies below 400 Hz. Looking at this from a "virtual microphone" perspective, the shelf-filtering produces virtual microphones with frequency dependent directivity: the virtual microphones get more hypercardioid at lower frequency.

While shelf-filtering is what must be done with regular speaker arrays in small spaces, like a living room, it's quite possibly not adequate in other situations. Irregular speaker arrays, like 5.1 surround, or large spaces that must accommodate more than a few people, can suffer from "reversed projection": because of the hypercardioid directionality of the virtual microphones, a given loudspeaker will always output some amount of information coming from the opposite (antipode) direction and with reversed polarity. There seems to be a consensus that decoding for larger spaces should avoid reversed projections. Decoding for these spaces must be then of the "in-phase" or "controlled opposite" type: the virtual microphones should not exhibit antipode information. In the first order, the cardioid microphone obeys this requirement with a null point at 180° from its apex.

Compared to an omnidirectional microphone, a first order cardioid has the following sensitivity characteristics: 0 dB (1) at 0°, -3 dB (1/√2 or 0.707) at 65.5°, -6 dB (0.5) at 90° and -infinity (0) at 180°. This cardioid becomes our reference for higher orders. When adding an order, the cardioid sensitivity of that order should diminish by 3 dB at 65.5° and by 6 dB at 90° compared to the previous order cardioid, while keeping the 180° null point. For example, a second-order cardioid has a sensitivity of -6 dB at 65.5° and -12 dB at 90°. By going to the fifth order, we can achieve a cardioid of -15 dB at 65.5° and -30 dB at 90°.

Our 5B2G decoder for 5.1 surround implements in-phase cardioid decoding with continuous variable control from first to fifth order.


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