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G.726 ADPCM codec. Theory of adaptive predictor coefficients

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vadkudr

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Dear colleagues,

Who knows background theory of G.726 codec related to adaptive predictor?
Can you describe (or link to) the theory answering to the questions:
1. How the structure of adaptive predictor was developed?
2. How coefficient adaptation rule was developed?
a1 (k) = (1 − 2^−8)a1 (k − 1) + (3 · 2^−8) sgn [p (k)] sgn [p (k − 1)]
a2 (k) = (1 − 2^−7)a2 (k − 1) + 2^−7 {sgn [p (k)] sgn [p (k − 2)]
− f [a1 (k − 1)] sgn [p (k)] sgn [p (k − 1)]}
bi (k) = (1 − 2^−9)bi (k − 1) + 2^−7 sgn [dq (k)] sgn [dq (k − i)].

Why these formulas are used?
 

wwfhm2002

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There is an IEEE paper on the history and development of ADPCM, name may be "theory analysis of ADPCM", I don't remember clearly.
 

vadkudr

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do you mean this paper?
Theoretical analysis of the ADPCM CCITT algorithm
Bonnet, M.; Macchi, O.; Jaidane-Saidane, M.
Communications, IEEE Transactions on
Volume 38, Issue 6, Jun 1990 Page(s):847 - 858
Digital Object Identifier 10.1109/26.57477
 

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