# Creating a Remote Choir Performance Recording Based on an Ambisonic Approach
## 3 Basics of Ambisonics  
Ambisonics was proposed by [PERSON], [PERSON], and [PERSON] in the early 1970s at the Universities of Oxford and Surrey [58]. Ambisonics refers to \"periphony\", a technique for reproducing sound both vertically and horizontally around the listener. As defined as follows: Ambisonics is a full-sphere surround sound format referring to a soundstage represented by a set of so-called spherical harmonics. In contrast to conventional stereo and surround formats (which rely on the principle of sending sound signals to specific speakers), ambisonics captures full directionality information for each sound wave that is captured by the microphone--including in the vertical plane [59]. In ambisonics, it is important to distinguish between the so-called A-Format and the B-Format. The A-Format is a microphone-specific recording of the signal--it is a direct recording of the signal coming from each microphone capsule. In this form, it is not yet usable, but each manufacturer provides methods for converting their microphone to the ambisonic domain, i.e., to B-Format. In B-Format, the following two methods of channel numbering are distinguished: FuMa (Furse-Malham) and ACN (Ambisonic Channel Number). FuMa numbering uses letter designations, and ACN numbering uses numerical designations; in addition, these channels are given in a different order. For example, the first row of ambisonics has four channels written in FuMa notation WXYZ (W--omni-directional, the so-called omni, X--forward-backward, Y--left-right, Z--up-down). In ACN notation, these channels will be 0, 3, 1, 2, respectively. The number of channels in 2D ambisonics is equal to 2N + 1, while in 3D ambisonics--respectively, as follows: (N + 1)2. Footnote 2: footnotemark:  
Figure 1 shows an illustration of sixteen (i.e., up to 3 rd order) spherical harmonics together with the FuMa and ACN ambisonic channel numbers. Moreover, worth mentioning are the recording formats, ranging from historical UHK to the following current ones: AMB--Microsoft Wave Format Extensible (WAVE-EX), a B-Format recording with the FuMa weighting factors. The main drawback of this file format based on the WAV container developed by Microsoft is the file size limitation of 4 GB. Ambisonic Exchange (AmbiX), on the other hand, uses Apple's (Core Audio Format) as a container. Figure 1: Illustration of spherical harmonics with the FuMa and ACN numbering corresponding to channels in ambisonics [60]. The channels are normalized according to the format in which the following signals are recorded:  
1. MaxN--normalizes each individual component not to exceed a gain of 1.0 for a panned mono source--used in FuMa;
2. N3D--similar to SN3D--orthonormal basis for 3D decomposition. Provides equal power to the encoded components for a perfectly scattered 3D field;
3. SN3D--(in ACN channel order) is widely used. Unlike N3D, no component will ever exceed the peak value of the 0 th order component for single point sources. This scheme has been adopted in the AmbiX coding format and is widely used. However, decoding includes algorithms and tools such as AllRAD [61]/AllRAD2 [62], Harpex [63], and DirAC [64; 65]. AllRAP (All-Round Ambisonic Panning) is an algorithm for arbitrary speaker arrangements aimed at creating apparent sources with stable loudness and adjustable width. The AllRAD (All-Round Ambisonic Decoding) method fits the ambisonic format concept. Conventional ambisonic decoding is straightforward only with optimal speaker settings, for which direction-independent energy and energy dissipation, estimated loudness, and width of the apparent source are obtained. The AllRAP/AllRAD algorithm is still simple but more versatile and uses a combination of virtual optimal loudspeaker settings with VBAP (Vector-Base Amplitude Panning). The Harpex (High Angular Resolution Planewave Expansion) decoder, on the other hand, is a tool that combines the spatial sharpness of parametric methods with the physical correctness of linear decoding without introducing audible artifacts.