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Joseph Nofech edited usepackage_amsmath_usepackage_makeroom_cancel__.tex
almost 8 years ago
Commit id: b386f122dbd2d314170c1285bea8346d8f60c3d0
deletions | additions
diff --git a/usepackage_amsmath_usepackage_makeroom_cancel__.tex b/usepackage_amsmath_usepackage_makeroom_cancel__.tex
index be21988..c4f4a96 100644
--- a/usepackage_amsmath_usepackage_makeroom_cancel__.tex
+++ b/usepackage_amsmath_usepackage_makeroom_cancel__.tex
...
&= \left< I_{signal}^2 - 2I_{signal}I'_{signal} + (I')_{signal}^2 + I_{noise}^2 - 2I_{noise}I'_{noise} + (I')_{noise}^2 \right> + \left< 2I_{signal}I_{noise} - 2I_{signal}I'_{noise} - 2I_{noise}I'_{signal} - 2I'_{signal}I'_{noise} \right> \\
&= \left< \left[ I_{signal} - I'_{signal} \right]^2 + \left[ I_{noise}^2 - I'_{noise} \right]^2 \right> + \left< 2I_{signal}I_{noise} - 2I_{signal}I'_{noise} - 2I_{noise}I'_{signal} - 2I'_{signal}I'_{noise} \right> \\
&= \left< \left[ I_{signal} - I'_{signal} \right]^2 \right> + \left< \left[ I_{noise}^2 - I'_{noise} \right]^2 \right> + \left< 2I_{signal}I_{noise} - 2I_{signal}I'_{noise} - 2I_{noise}I'_{signal} - 2I'_{signal}I'_{noise} \right> \\
&\approx \left< \left[ I_{signal} - I'_{signal} \right]^2 \right> + \left< \left[ I_{noise}^2 - I'_{noise} \right]^2
\right> + \left< 2I_{signal}I_{noise} - 2I_{signal}I'_{noise} - 2I_{noise}I'_{signal} - 2I'_{signal}I'_{noise} \right> \\ \right>\\
&\approx S_{2(signal)} + S_{2(noise)}
\end{align*}
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