Synthesis of 4-2-4 Matrix Recording Systems

White JV. Synthesis of 4-2-4 Matrix Recording Systems. J Audio Eng Soc. 1976;24(4):250-257. Available from: https://aes.org/publications/elibrary-page/?id=2625

@article{White1976_2625,
  author = {White, James V.},
  title = {{Synthesis of 4-2-4 Matrix Recording Systems}},
  journal = {Journal of the Audio Engineering Society},
  volume = {24},
  number = {4},
  pages = {250--257},
  year = {1976},
  month = may,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=2625}
}

TY  - JOUR
TI  - Synthesis of 4-2-4 Matrix Recording Systems
AU  - White, James V.
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 24
IS  - 4
SP  - 250
EP  - 257
PY  - 1976
DA  - 1976/05/06
UR  - https://aes.org/publications/elibrary-page/?id=2625
PB  - Audio Engineering Society
LA  - en
AB  - Linear time-invariant 4-2-4 matrix recording systems are defined mathematically. Mono and stereo compatibility objectives are states; the class of compatible encoders is then synthesized that meets these objectives. To each of these encoders there corresponds a decoder that yields the smallest possible mean-square error in its quadraphonic outputs. An explicity formula for this minimum-error decoder is derived, which shows that the minimum-error decoder is time varying (uses -logic- to track the correlations of the quadraphonic signals). The optimal time-invariant (no logic) decoder, which minimizes the mean-square error for worst case inputs, is then synthesized, and several of its most important properties are discussed. The conditions for optimum time-invariant decoding are then combined with the conditions for compatible encoding; this yields the class of optimized compatible recording systems, which is termed the SQ family. Two well-known members of this family are basic SQ and forward-oriented SQ.
ER  -