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Approximating the magnitude of a complex number $Z=I+jQ$ as: $$|Z| \approx \alpha \max(|I|, |Q|) + \beta \min(|I|, |Q|)$$ looks a lot to me as some standard diagonal approximation found in engineer books, before calculators. For instance in "Notes et formules de l'ingénieur of De Laharpe" (my 1923 edition below) you find the approximation, for $...


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Average error is no way close to 0.6%. Why would it be? Even the most casual inspection shows that the error will much bigger. Let's look at a simple 45 degree angle. Let's assume $z = 1 + i$ and so $|z| = \sqrt{2}$. The algorithm would estimate this as $|z|' = 1 + 0.25 = 1.25$, which is off by about 11.6% or -18.7dB, which is what the author quoted.


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