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Refining the transformation matrices

The 6x6 transformation to ITU 5.1/6.1 described above with a headroom margin of 6dB has the possibility of clipping.  However unlikely to be noticeable, with a safety factor of 0.5, random phase components could add instantaneously to 117% in the L or R channels.  The safety gain of 0.5 also lowers L & R replay levels 6dB.  Furthermore, the 6x6 matrix reconstitution of PerAmbio, where the safety gain of 0.5 is made up, causes loss of SNR of a minimum of 6dB to a maximum 9.8dB, or from 1 bit to just over 1.6 of 24 bits.  In addition, the six tilt and untilt matrices for i, j, & k are all different.

There is a solution: Since Ambiophonicsí has high localization accuracy horizontally, and because it involves crosstalk cancellation, it is advisable to assign only the Ambio pair to L,R and not include Ambisonic information.  This prevents conflicting imaging cues arriving at L,R speakers from two different pickup systems.  Whether a price, believed to be acceptable, is paid in reducing the number of speakers reproducing ambience information from six to four in 2D requires further investigation (eight or more speakers are used for ambience in 3D).  Also since Ambiophonics is largely insensitive to a change in inclination over the range of angles normally associated with tilting, say 0 to ñ45ƒ, the Ambisonic components may be electrically tilted independently over this range.

The preceding suggests simplifying both the transformation matrix {S} and reconstituting matrix {P} from 6x6 to 4x4, reducing the number of DSP coefficients from 36 to 16 as shown in Table 7 & 8.  Tilt matrix {Bí} and ìuntiltî matrix {B} are now also 4x4 and are respectively the same for all modes, as in Table 9 & 10.  With no ambience added to L,R there is no opportunity for clipping during transformation of random phase components.  Furthermore, during reconstitution of PerAmbio 3D, noise from making up the more gentle safety factor of 0.85 results in loss of SNR of only 1.4dB for modes i, ií, j, & jí and no more than 3dB for k & kí, which is just over ‡ of 24 bits lost for these two modes.  L,R levels are now reduced only 1.4dB compared to 6dB for 6x6 matrices. The 4x4 transformation modes are shown in Fig. 6 & 7.

Table 7. 4x4 matrix {S} (lightly shaded) transforms six-channel PerAmbio 3D into one of three modes Ií, jí, or kí for ITU 5.1/6.1 replay without a decoder, or with a converter back to PerAmbio 3D.

Table 8. 4x4 matrix {P} (lightly shaded) reconstitutes six PerAmbio 6.1.10+ channels without loss for fully periphonic 3D surround.

Table 9. 4x4 {Bií} matrix ìtiltsî recording modes ií, jí, or kí for ITU 5.1/6.1 replay.  Any angle may be used (-30ƒ shown).

Table 10.  4x4 {B} matrix ìuntiltsî back to horizontal B-format recording modes ií, jí, or kí for PerAmbio 3D (+30ƒ shown).

 

Fig.6  illustrates in terms of elevation three basic modes I, j, & k for 4x4 transformation to ITU 5.1/6.1 of amphitheater, concert with soloist & audience, and arena.  Source is to the right.

Fig.7 shows three ìtiltedî modes ií, jí, & kí for 4x4 transformation to 5.1/6.1 of opera, drama, and organ behind choir. Source is to the right.

The revised 4x4 transformation matrix {S} with ñ30ƒ tilt is shown in Table 11.  The new 4x4 reconstitution matrix {P} with +30 ìuntiltî is shown in Table 12.

Table 11.  4x4 matrix {Sí} (lightly shaded) transforms six PerAmbio 3D channels into one of three modes Ií, jí, or kí for standard ITU 5.1/6.1 replay without a decoder (ñ30ƒ tilt shown).

Table 12. 4x4 matrix {Pí} reconstitutes six PerAmbio 6.1.10+ channels without loss and restores any tilt for periphonic 3D replay (+30ƒ shown).

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