Banger added

This commit is contained in:
Marius Drechsler 2024-07-22 21:05:16 +02:00
parent 0cc1e27cb5
commit dbce6aa469
2 changed files with 19 additions and 2 deletions

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@ -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],
[$bold(phi_"max,odd")$],[$1/24$],[$1/20$],[$3/56$],[$1/18$]
),
)<tb:>
$
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"
$

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