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Remove reference to alpha-max beta-min magnitude calculation.
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bemasher committed Aug 18, 2016
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13 changes: 1 addition & 12 deletions docs/signal.md
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Expand Up @@ -25,18 +25,7 @@ The signal is made up of interleaved in-phase and quadrature samples, 8-bits per
$$\vert z\vert = \sqrt{\Re(z)^2 + \Im(z)^2}$$
</div>

To meet performance requirements the magnitude computation has two implementations. The first uses a pre-computed lookup table which maps all possible 8-bit values to their floating-point squares. Calculating the magnitude using the lookup table then only involves two lookups, one addition and one square-root.

The second implementation is an approximation known as Alpha-Max plus Beta-Min whose efficiency comes from eliminating the square root operation:

<div>
$$
\begin{aligned}
&\alpha = \frac{2\cos\frac{\pi}{8}}{1+cos\frac{\pi}{8}} \qquad \beta = \frac{2\sin\frac{\pi}{8}}{1+cos\frac{\pi}{8}} \\ \\
\vert z\vert \approx \,&\alpha\cdot\max(\Re(z),\Im(z)) + \beta\cdot\min(\Re(z),\Im(z))
\end{aligned}
$$
</div>
To meet performance requirements the magnitude computation is done using a pre-computed lookup table which maps all possible 8-bit values to their floating-point squares. Calculating the magnitude using the lookup table then only involves two lookups, one addition and one square-root.

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