From dbce6aa469dd46167b6110dc3dad38fc4106c9f3 Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Mon, 22 Jul 2024 21:05:16 +0200 Subject: [PATCH] Banger added --- content/SMHD.typ | 21 +++++++++++++++++++-- main.pdf | Bin 555146 -> 556973 bytes 2 files changed, 19 insertions(+), 2 deletions(-) diff --git a/content/SMHD.typ b/content/SMHD.typ index 831b31b..b21751d 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -295,10 +295,27 @@ Here, we multiply @eq:offset with the maximum offsetting index $i_"max" = s/2$. Now, if we want to find the maximum offset for a odd number of metrics, we need to modify @eq:max_offset_even, more specifically its numerator. We know, that we need to keep the original quantizer for a odd number of metrics, besides that, the method stays the same. -For that reason, we will decrease the parameter $m$ by $1$: +For that reason, we will decrease the parameter $m$ by $1$, that way we will still perform a division without remainder: + $ -phi_"max_odd" &= frac(frac(m-1, 2), 2^n dot m dot 2)\ +phi_"max,odd" &= frac(frac(m-1, 2), 2^n dot m dot 2)\ &= lr(frac(m-1, 2^n dot m dot 4)mid(|))_(n=2, m=3) = 1/24 $ +It is important to note, that $phi_"max,odd"$, unlike $phi_"max,even"$ is dependent on the parameter $m$. + +#figure( + table( + columns: (5), + align: center + horizon, + inset: 7pt, + [*m*],[3],[5],[7],[9], + [$bold(phi_"max,odd")$],[$1/24$],[$1/20$],[$3/56$],[$1/18$] + ), +) + +$ +lim_(m arrow.r infinity) phi_"max,odd" &= frac(m-1, 2^n dot m dot 4)\ +&= frac(1, 2^n dot 4) = phi_"max,even" +$ diff --git a/main.pdf b/main.pdf index 7947345b00b59eeb717b850ab77b9e0129b5553b..e5ec858b5ec6551865682d54ef97a90344a77dd3 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