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Exact MSRE of Log-Uniform Quantization

For a log-uniform quantizer cell with common ratio r and geometric midpoint, the exact MSRE is 2 − 2√r·ln(r)/(r−1). Taylor expansion: ε²/12 − 7ε⁴/2880 + O(ε⁶), confirming the high-resolution approximation and correcting an earlier erroneous ε²/2 result (factor of 6 error). Lean 4 verified.

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Type
theorem
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public
Published
Mar 27, 2026
Last updated
Mar 27, 2026

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exact-formulalean-verifiedMSREquantizationtheorem