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Audio Engineering Society
Convention Paper

Transforming Ambiophonic + Ambisonic 3D Surround Sound to & from ITU 5.1/6.1
Robert E. (Robin) Miller III 20031


Page 3 -- Basic PerAmbio Recording Modes: i, j, k

Since ITU 5.1/6.1 is to be derived from 3D recordings - and since recording venues vary in their 3D space - the recordist must have control of how the 3D space for each recording is translated into the best result in 2D.  Then in the end, it must be possible to reconstitute the 3D signals without loss.

The method provides the recording engineer with six acoustically based variations.  In the interest of continuity in describing the matrix transformations, the six acoustic modes will be more fully described later.  Experimental PerAmbio 6.1.10+ recordings have been made of a number of musical genres and venues both to verify the concept and to demonstrate it to so engineers can evaluate the results.

In order to be able to reconstitute height, one or more channels must be non-coplanar with the other channels.  While there might be something to be said for having C coplanar with L & R, the argument is made (and results support) that C need not be coplanar with L & R.  Nor need SC be coplanar with SL & SR.  For 3D, non-coplanar channels increase height gain, thereby decreasing noise during rematrixing.  Results in 2D are optimal because desirable non-co-planar sounds of the venue can be favored, e.g. ceiling ambience or upstage voices.  In 5.1 this "compromise" is quite acceptable, since height is not reproduced in any case.  In both 2D and 3D, any channel that is not coplanar with any other contributes spaciousness because the signals have greater probability of being decorrelated.  Finally in 3D, human hearing resolves more acutely horizontally than vertically.

Fig.4  Illustrates in terms of elevation three basic modes I, j, & k for  transformation to ITU 5.1/6.1 of amphitheater, concert with soloist & audience, and arena.  Source is to the right.

Fig.5  Shows in elevation three tilted modes i, j, & k for transformation to 5.1/6.1 of opera, drama, and organ behind choir. Source is to the right.

Three basic modes are shown in Fig. 4, and variants that place the microphone array high and tilted in Fig. 5.  Their applications will be described in more detail later, but range from recording opera to broadcasting sports in dual format 2D & 3D surround.

The 6x6 matrices Si, Sj, and Sk for transforming PerAmbio to ITU 6.1 are shown in Table 1, with mode elevation angles on the left.  PerAmbio reconstitution matrices Pi, Pj, and Pk are shown in Table 2, with confirmation on the right that Pout=Pin for normalized full scale random phase addition of a sound emanating from 45° front, 45° left, and 45° up.

Table 1.  Matrix {S} coefficients to transform six PerAmbio channels in one of three modes i, j, or k into ITU-compatible form for replay without a decoder on standard 5.1/6.1 layouts.  When desired, the six original PerAmbio channels can be recovered without loss for a 3D layout.

Table 2. PerAmbio reconstitution matrix {P}, by which the six original channels can be recovered for fully periphonic 3D surround.

Initially, Gerzon TriField coefficients were used to derive Center information from L & R [16], but redundant results conflicted with the frontal imaging of the hybrid approach, along with narrowing the front stage, especially when played Ambiophonically.

Correcting 5.1/6.1 Speaker Placement

No decoder is necessary for normal 5.1/6.1 replay.  However, a smart decoder would allow users to correct for non-standard speaker placements in ways not possible with conventional multichannel recordings.  In this case, PerAmbio would be reconstituted as though for 3D, but then re-transformed with differing speaker azimuths and elevations.

Digitally Tilting 3D Space - Modes i, j, k

Tilting the Ambisonic image offers the recording engineer flexibility, doubling the number of applicable transformation modes, and aligning the Ambisonic image vertically with the L,R image.  Tilting is usually associated with raising the microphone, suspended or on a high stand.  Lower gives more the perspective of sitting in a front row, while raised gives a balcony perspective and puts the microphone above audience and camera sight lines.  Raised and in 3D, we can discern vertical localization of upstage v. downstage sources, such as pit orchestra v. singers, organ above chorus, playing field sounds below crowd, etc.  Tilting does not necessarily mean physically tilting the array, but electrically changing an Ambisonic arrays angle of inclination, elevation Φ, using a tilting matrix designated {B}.

Using Ambisonic B-format, tilting at angle Φ° from horizontal can be implemented either during recording or in postproduction using

w' = w

x' = x*cos Φ° + z*sin Φ°

y' = y

z' = z*cos Φ° - x*sin Φ°

Or in matrix form by tilting {S} to {S} by {B}

{S} = {B} {S}

For correct horizontal orientation of the reconstituted Ambisonic B format, an untilting matrix must be employed upon replay

w = w

x = x*cos Φ° + z*sin Φ°

y = y

z = z*cos Φ° - x*sin Φ°

Or in matrix form, untilting the PerAmbio 3D reconstitution matrix {P} is the inverse of untilting {S}

{P} = { {B}-1 {S} }-1

As examples, for mode i the 6x6 tilting matrix {Bi} is shown for -30° tilt in Table 3.  The untilting inverse matrix {Bi}={Bi}-1 is shown for +30° in Table 4.  Transformation to 2D ITU5.1/6.1 with a -30° tilt is shown in Table 5.  Reconstitution of PerAmbio 3D by +30° untilting back to horizontal is in Table 6.

Table 3. Tilting matrix {Bi} for tilting the mode i soundscape -30° provides three additional recording modes i, j, or k.

Table 4. Untilting matrix {Bi} restores to horizontal six discrete transformed channels on DVD-A, SACD, or DTS-CD (+30° shown).

Table 5.  {S} matrix coefficients transform six PerAmbio channels according to one of three tilted modes I, j, or k into ITU-compatible form for replay without a decoder for 5.1/6.1 layouts (-30° tilt shown).

Table 6. {P} matrix reconstitutes original PerAmbio 6.1.10+ channels for full periphonic 3D surround and untilts to horizontal (+30° shown).

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