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Glossary of some relevant Ambisonic and Ambisonic Toolkit words

- A-format
- Component or signal set in the
*angular domain*, evenly distributed across the surface of the sphere in a*spherical design*. Within the context of the Ambisonic Toolkit, any required equalisation or radial filtering is expected to have been applied. In other words, the Ambisonic Toolkit views*A-format*as a uniform spherical decomposition of the soundfield. - AL degree (ℓ)
*Associated Legendre*degree. A complete coefficient set of a given*Ambisonic order*n includes*AL degrees*ℓ <= n. See Associated Legendre polynomials- AL index (m)
*Associated Legendre*index. (Confusingly, also known as*Associated Legendre*order.) In conjunction with*Associated Legendre*degrees references individual*spherical harmonic*components, in the form (ℓ, m).*Associated Legendre*indices range |m| <= ℓ for a complete coefficient set of a given degrees. See Associated Legendre polynomials- acoustic admittance
- Vector quantity, reciprocal of
*acoustic impedance*, which may be regarded as a normalised form of*sound intensity*. See Acoustic impedance. - acoustic wavenumber
- Spatial frequency of a sound wave, measured in radians per meter.
- active
- Describes the real,
*in phase*, part of a complex soundfield. See also*reactive*. - Ambisonic equivalent panning (AEP)
- Complete the Ambisonic
*panning law*by combining Ambisonic*encoding*and*decoding*into a single operation. - Ambisonic order
- Specifies the maximum
*AL degree*, ℓ, of a given signal set. - angular domain
- Information represented in terms of angular
*basis functions*. - Associated Legendre functions (AL)
- The well-behaved solutions of the general Legendre equation, which play an important role in the definition of
*spherical harmonics*. See Associated Legendre polynomials - B-format
- Component or signal set in the
*spherical domain*. In classic*first order Ambisonics*, aka Gerzonic, B-format indicates a signal encoded where Ambisonic order n = 1, and components are ordered and normalised by the (now named) Furse-Malham and MaxN conventions.*B-format*is often used to indicate any Ambisonic signal set, without regard to Ambisonic order, component ordering or normalisation. - basic
- Ambisonic Toolkit soundfield designation. A signal, transform or coefficient set with all real modal components.
- basic wave
- Ambisonic Toolkit soundfield designation. A travelling wave encoded with all real modal components. I.e., a travelling wave encoded at the
*reference radius*. - basis function
- An element of a particular basis for a function space. See Basis function.
- beam
- Window in the spatial domain.
- component normalisation
*Spherical harmonic*coefficient normalisation convention. E.g., maxN, N3D, SN3D. See normalisation.- component ordering
- Sorting or ordering convention applied to arrange spherical harmonic encoding coefficients and resulting signal sets. E.g., Furse-Malham (FuMa), Ambisonic Channel Number (ACN), Single Index Designation (SID). See ordering.
- decode
- Transform a
*spherical domain*signal to the angular domain. Decoding is the end of the Ambisonic panning law. - decoding radius
- The radius at which a given signal set is decoded to the
*angular domain*. If no*radial filter*is applied, the decoding is described as*basic*, and as a result is decoded at the*reference radius*. - diffuse field
- Complex isotropic soundfield.
- dimensions
- Two dimensional (2D),
*pantophonic*, or three dimensional (3D),*periphonic*.NOTE: The Ambisonic Toolkit does not offer*mixed order*encoding or decoding. - effective radius
- Radius of the volume (or area) of exact soundfield reconstruction.
- encode
- Transform a signal set into the
*spherical domain*. Encoding is the beginning of the Ambisonic panning law. - encoding radius
- The radius at which a given signal set is encoded into the
*spherical domain*. If no*radial filter*is applied, the encoding is described as*basic*, and as a result is encoded at the*reference radius*. - energy localisation vector (rE)
- Vector quantity offering an estimate of the perceived localisation of a phantom source in terms of energy, expected to predict imaging between 500 and 5000 Hz.
- far-field
- Characterized by a minimally
*reactive**travelling wave*. I.e., a wave with minimal quadrature components. A*planewave*is in the*far-field*. See also*near-field*. - First Order Ambisonics (FOA)
- Ambisonics employing components up to
*AL degrees*ℓ <= 1. - focused source
- Phantom image appearing within the radius of the reproducing loudspeaker array.
- format
- Ambisonic Toolkit designation indicating Ambisonic
*component ordering*and*component normalisation*. E.g., ACN-N3D. - Gerzon energy vector
- See
*energy localisation vector*. - Higher Order Ambisonics (HOA)
- Ambisonics employing components up to
*AL degrees*ℓ <=*Ambisonic order*n. - holographic
- Capable of capturing, reproducing or otherwise synthesizing the complex features of a soundfield, including the
*sound pressure*field,*particle velocity*field, and*sound intensity*field. - holophonic
- See
*holographic*. - image
- Synthesize, modify or otherwise control the phantom images generated by a panning law.
- isotropic
- Uniform in all directions.
- kind
- Ambisonic Toolkit operation ID, e.g.,
`\quad`

. - look direction
- The perceived localisation direction a listener would identify as a source origin.
- Makita localisation vector
- See
*velocity localisation vector*. - near-field
- Characterized by a highly
*reactive**travelling wave*, where*active*and*reactive intensity*vectors are aligned. A*spherical wave*is in the*near-field*. See also*far-field*. - near-field compensated (NFC)
- In classic Gerzonic
*first order Ambisonics*,*near-field compensation*describes the*near-field control*applied to accommodate for decoding loudspeakers placed at finite radii. I.e.,*near-field compensation*compensates for the fact real loudspeakers cannot be placed at the infinite*reference radius*of Gerzonic*Ambisonics*.NOTE: The Ambisonic Toolkit's`\FOA`

set observes this convention. - near-field controlled (NFC or NFCtrl)
- Characterizing the synthesis or control of a soundfield with near-field properties. Implemnted via
*radial filtering*. The explicit use of the term*control*is preferred to avoid confusion with the classic Gerzonic use of the term*near-field compensated*.NOTE: The Ambisonic Toolkit's`\HOA`

sets observes this convention. - near-field effect (NFE)
- See
*near-field*and*near-field controlled*. - operation (op)
- Ambisonic Toolkit designation indicating the processing domain of an Ambisonic signal set transform:
`\matrix`

or`\kernel`

. - panning law
- Algorithm for generating phantom imaging.
- particle velocity
- Vector quantity specifying the velocity of a particle in a medium as it transmits a wave. Ambisonic components of
*AL degree*ℓ = 1 are proportional to*particle velocity*. See Particle velocity. - planewave
- A travelling wave with an infinite radial component.
- radial filter
- Transform modifying the radial encoding of an Ambisonic signal.
*Radial filtering*is required to implement the*near-field effect*. - reactive
- Describes the imaginary,
*in quadrature*, part of a complex soundfield. See also*active*. - reference radius
- Encoding radius where all modal components are real. See also
*basic*and*basic wave*. - sectoral modes
- Spherical modes where
*AL degree*and*AL index*are related ℓ = |m|. These modes encode azimuth. See Visualization of the spherical harmonics and Sectorial Harmonic. - set
- Ambisonic Toolkit designation indicating
*Ambisonic order*and encoding*format*. E.g.,`\FOA`

,`\HOA3`

. - sound intensity
- Vector quantity specifying sound power per unit area. See Sound intensity.
- sound pressure
- Quantity specifying the local pressure deviation caused by a sound wave. The Ambisonic component of AL degree ℓ = 0 is proportional to
*sound pressure*. See Sound pressure. - soundfield
- Region of an elastic medium containing sound waves. See Sound fields.
- soundfield kernel composition
- An idiomatic composition strategy addressing the holistic problem of creatively controlling a complete soundfield for aesthetic purposes. The Ambisonic Toolkit is designed to facilitate this paradigm.
- spherical coefficient
- Real or complex scalar applied to
*encode*a signal set into the*spherical domain*. See*spherical harmonic*. - spherical design
- Minimal equal-weight quadrature on S^d. See Spherical design.
- spherical domain
- Information represented in terms of spherical
*basis functions*. See*spherical harmonics*. - spherical harmonics (SH)
- A complete set of orthogonal, Fourier
*basis functions*on the sphere. For Ambisonics, a set of real form harmonics truncated to a highest*Associated Legendre*degree, i.e., a given*Ambisonic order*, encodes a soundfield. See Spherical harmonics. - spherical modes
- See
*spherical harmonics*. - spherical wave
- A travelling wave with a finite radial component, i.e., a
*point source*. - standing wave
- A stationary wave.
- tesseral modes
- Spherical modes not included as
*sectoral*or*zonal*, encoding both azimuth and elevation. See Visualization of the spherical harmonics and Tesseral Harmonic. - transform
- Modify a
*spherical domain*signal in the*spherical domain*. - travelling wave
- A propagating, incidental wave arriving from some direction. A travelling wave has a
*look direction*. - type
- Ambisonic Toolkit soundfield operation designation. E.g.,
`\encode`

,`\xform`

,`\decode`

. - velocity localisation vector (rV)
- Vector quantity offering an estimate of the perceived localisation of a phantom source at low frequency, predicting imaging up to around 1.5 kHz. Can be found as the real part of
*acoustic admittance*, the*active acoustic admittance*. - zonal modes
- Spherical modes where
*AL index*m = 0. These modes encode elevation. See Visualization of the spherical harmonics and Zonal Harmonic.

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