# LaTeX2HTML 2023 (Released January 1, 2023)
# Associate images original text with physical files.


$key = q//;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 15.37ex; vertical-align: -12.78ex; " SRC="|."$dir".q|img99.svg"
 ALT="\fbox{
\begin{minipage}[t]{12cm}
\textsf{Averaged channel intensity and weight (...
...w_{T'}(i)} \\\\
w_S(i) &amp; = &amp; w_{R'}(i) + w_{T'}(i)
\end{eqnarray}\end{minipage}}">|; 

$key = q/(N-1)^{th};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.78ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img13.svg"
 ALT="$(N-1)^{th}$">|; 

$key = q/-ctimesf_{{ensuremath{mathrm{res}}{,S_{{ensuremath{mathrm{out}}{}}slashf_{{ensuremath{mathrm{rest}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img120.svg"
 ALT="$-c \times f_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}} /
f_{\ensuremath{\mathrm{rest}},S_{\ensuremath{\mathrm{out}}}} $">|; 

$key = q/-f_{{ensuremath{mathrm{rest}}{,S_{{ensuremath{mathrm{out}}{}}timesv_{{ensuremath{mathrm{res}}{,S_{{ensuremath{mathrm{out}}{}}slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img127.svg"
 ALT="$- f_{\ensuremath{\mathrm{rest}},S_{\ensuremath{\mathrm{out}}}} \times v_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}} / c $">|; 

$key = q/0.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.72ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img75.svg"
 ALT="$0.0$">|; 

$key = q/0.25;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.72ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img76.svg"
 ALT="$0.25$">|; 

$key = q/0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.72ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img77.svg"
 ALT="$0.5$">|; 

$key = q/0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.72ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img27.svg"
 ALT="$0$">|; 

$key = q/0<f(j)<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img56.svg"
 ALT="$0 &lt; f(j) &lt; 1 $">|; 

$key = q/1.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.72ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img96.svg"
 ALT="$1.0$">|; 

$key = q/1slash{sigma}^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.69ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img10.svg"
 ALT="$1/{\sigma}^2$">|; 

$key = q/N(mu_R,{sigma_R}^2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.69ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img45.svg"
 ALT="$N(\mu_R,{\sigma_R}^2)$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img25.svg"
 ALT="$N$">|; 

$key = q/N^{th};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.20ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img14.svg"
 ALT="$N^{th}$">|; 

$key = q/N_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.16ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img32.svg"
 ALT="$N_S$">|; 

$key = q/R';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.97ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img36.svg"
 ALT="$R'$">|; 

$key = q/R'rightarrowR'';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.97ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img93.svg"
 ALT="$R' \rightarrow R''$">|; 

$key = q/R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3.svg"
 ALT="$R$">|; 

$key = q/S(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img42.svg"
 ALT="$S(i)$">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img12.svg"
 ALT="$S$">|; 

$key = q/S_{{ensuremath{mathrm{in}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.16ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img103.svg"
 ALT="$S_{\ensuremath{\mathrm{in}}}$">|; 

$key = q/S_{{ensuremath{mathrm{out}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.16ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img104.svg"
 ALT="$S_{\ensuremath{\mathrm{out}}}$">|; 

$key = q/T';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.97ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img37.svg"
 ALT="$T'$">|; 

$key = q/T(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img33.svg"
 ALT="$T(i)$">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4.svg"
 ALT="$T$">|; 

$key = q/T_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.16ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img43.svg"
 ALT="$T_R$">|; 

$key = q/T_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.16ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img97.svg"
 ALT="$T_S$">|; 

$key = q/T_{R'}(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img61.svg"
 ALT="$T_{R'}(i)$">|; 

$key = q/T_{{ensuremath{mathrm{sys}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.48ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img107.svg"
 ALT="$T_{\ensuremath{\mathrm{sys}},S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/T_{{ensuremath{mathrm{sys}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.48ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img9.svg"
 ALT="$T_{\ensuremath{\mathrm{sys}}}$">|; 

$key = q/X;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img71.svg"
 ALT="$X$">|; 

$key = q/Y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.81ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img72.svg"
 ALT="$Y$">|; 

$key = q/[x_{{ensuremath{mathrm{min}}{,S},x_{{ensuremath{mathrm{max}}{,S}];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img31.svg"
 ALT="$[x_{\ensuremath{\mathrm{min}},S},x_{\ensuremath{\mathrm{max}},S}]$">|; 

$key = q/^1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1.svg"
 ALT="$^1$">|; 

$key = q/^{1,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2.svg"
 ALT="$^{1,2}$">|; 

$key = q/^{primeprime};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.97ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img101.svg"
 ALT="$^{\prime\prime}$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img69.svg"
 ALT="$a$">|; 

$key = q/alpha(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img58.svg"
 ALT="$\alpha(j)$">|; 

$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img70.svg"
 ALT="$b$">|; 

$key = q/beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img57.svg"
 ALT="$\beta$">|; 

$key = q/c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img121.svg"
 ALT="$c$">|; 

$key = q/displaystyleN_S={ensuremath{mathrm{int}}{(frac{x_{{ensuremath{mathrm{max}}{,S}-x_{{ensuremath{mathrm{min}}{,S}}{r_S}+1.5),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.08ex; vertical-align: -2.06ex; " SRC="|."$dir".q|img26.svg"
 ALT="$\displaystyle N_S = \ensuremath{\mathrm{int}}( \frac{x_{\ensuremath{\mathrm{max}},S}-x_{\ensuremath{\mathrm{min}},S}}{r_S} + 1.5),
$">|; 

$key = q/displaystyleT_{R'}(i)=sum_{j=j_{{ensuremath{mathrm{min}}{}}^{j_{{ensuremath{mathrm{max}}{}}alpha_R(j)timesT_R(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.81ex; vertical-align: -3.40ex; " SRC="|."$dir".q|img62.svg"
 ALT="$\displaystyle T_{R'}(i) = \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} \alpha_R(j) \times T_R(j)
$">|; 

$key = q/displaystylealpha_R(j)=frac{f_R(j)timesw_R(j)}{beta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.57ex; vertical-align: -2.16ex; " SRC="|."$dir".q|img60.svg"
 ALT="$\displaystyle \alpha_R(j) = \frac{f_R(j) \times w_R(j)}{\beta}$">|; 

$key = q/displaystylebeta=sum_{j=j_{{ensuremath{mathrm{min}}{}}^{j_{{ensuremath{mathrm{max}}{}}f_R(j)timesw_R(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.81ex; vertical-align: -3.40ex; " SRC="|."$dir".q|img59.svg"
 ALT="$\displaystyle \beta = \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j) \times w_R(j)$">|; 

$key = q/displaystylefrac{1}{beta^2}sum_{j=j_{{ensuremath{mathrm{min}}{}}^{j_{{ensuremath{mathrm{max}}{}}f_R(j)^2,w_R(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.81ex; vertical-align: -3.40ex; " SRC="|."$dir".q|img67.svg"
 ALT="$\displaystyle \frac{1}{\beta^2}
\sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j)^2   w_R(j)$">|; 

$key = q/displaystyler_S={ensuremath{mathrm{max}}{(|r_R|,|r_T|);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle r_S = \ensuremath{\mathrm{max}}(\vert r_R\vert,\vert r_T\vert)
$">|; 

$key = q/displaystylesum_{j=j_{{ensuremath{mathrm{min}}{}}^{j_{{ensuremath{mathrm{max}}{}}alpha_R(j)^2times{ensuremath{mathrm{var}}{left(T_R(j)right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.81ex; vertical-align: -3.40ex; " SRC="|."$dir".q|img66.svg"
 ALT="$\displaystyle \sum_{ j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}}
\alpha_R(j)^2 \times \ensuremath{\mathrm{var}} \left( T_R(j) \right)$">|; 

$key = q/displaystylet_{S_{{ensuremath{mathrm{out}}{}}=t_{S_{{ensuremath{mathrm{in}}{}}+t_{{ensuremath{mathrm{obs}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img106.svg"
 ALT="$\displaystyle
t_{S_{\ensuremath{\mathrm{out}}}} = t_{S_{\ensuremath{\mathrm{in}}}} + t_{\ensuremath{\mathrm{obs}}}
$">|; 

$key = q/displaystylew_R(i)=frac{1}{{sigma_R}(i)^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.45ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img51.svg"
 ALT="$\displaystyle
w_R(i) = \frac{1}{{\sigma_R}(i)^2}
$">|; 

$key = q/displaystylex_{{ensuremath{mathrm{max}}{,S};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\displaystyle x_{\ensuremath{\mathrm{max}},S}$">|; 

$key = q/displaystylex_{{ensuremath{mathrm{min}}{,S};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img18.svg"
 ALT="$\displaystyle x_{\ensuremath{\mathrm{min}},S}$">|; 

$key = q/displaystylex_{{ensuremath{mathrm{val}}{,S}=x_{{ensuremath{mathrm{min}}{,S}-1.timesr_S,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.39ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\displaystyle x_{\ensuremath{\mathrm{val}},S} = x_{\ensuremath{\mathrm{min}},S} - 1. \times r_S,
$">|; 

$key = q/displaystyle{ensuremath{mathrm{max}}{(x_{{ensuremath{mathrm{max}}{,R},x_{{ensuremath{mathrm{max}}{,T});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{max}}( x_{\ensuremath{\mathrm{max}},R} , x_{\ensuremath{\mathrm{max}},T} )$">|; 

$key = q/displaystyle{ensuremath{mathrm{max}}{(x_{{ensuremath{mathrm{min}}{,R},x_{{ensuremath{mathrm{min}}{,T});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{max}}( x_{\ensuremath{\mathrm{min}},R} , x_{\ensuremath{\mathrm{min}},T} )$">|; 

$key = q/displaystyle{ensuremath{mathrm{min}}{(x_{{ensuremath{mathrm{max}}{,R},x_{{ensuremath{mathrm{max}}{,T});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{min}}( x_{\ensuremath{\mathrm{max}},R} , x_{\ensuremath{\mathrm{max}},T} )$">|; 

$key = q/displaystyle{ensuremath{mathrm{min}}{(x_{{ensuremath{mathrm{min}}{,R},x_{{ensuremath{mathrm{min}}{,T});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.63ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{min}}( x_{\ensuremath{\mathrm{min}},R} , x_{\ensuremath{\mathrm{min}},T} )$">|; 

$key = q/displaystyle{ensuremath{mathrm{pdf}}{_R(x)=frac{1}{sigma_Rsqrt{2pi}},{ensuremath{mathrm{exp}}{left(-frac{(x-mu_R)^2}{2{sigma_R}^2}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.88ex; vertical-align: -2.32ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{pdf}}_R(x) = \frac{1}{\sigma_R \sqrt{2 \pi}}  
\ensuremath{\mathrm{exp}} \left( - \frac{(x-\mu_R)^2}{2 {\sigma_R}^2} \right)
$">|; 

$key = q/displaystyle{ensuremath{mathrm{var}}{(T_R(i))={sigma_R}(i)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.81ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img49.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{var}}(T_R(i)) = {\sigma_R}(i)^2
$">|; 

$key = q/displaystyle{ensuremath{mathrm{var}}{(T_{R'}(i));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img64.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{var}}(T_{R'}(i))$">|; 

$key = q/displaystyle{ensuremath{mathrm{var}}{(aX+bY)=a^2{ensuremath{mathrm{var}}{(X)+b^2{ensuremath{mathrm{var}}{(Y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.81ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img68.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{var}} (aX+bY) = a^2 \ensuremath{\mathrm{var}}(X) + b^2 \ensuremath{\mathrm{var}}(Y)
$">|; 

$key = q/displaystyle{ensuremath{mathrm{var}}{left(sum_{j=j_{{ensuremath{mathrm{min}}{}}^{j_{{ensuremath{mathrm{max}}{}}alpha_R(j)timesT_R(j)right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.56ex; vertical-align: -3.72ex; " SRC="|."$dir".q|img65.svg"
 ALT="$\displaystyle \ensuremath{\mathrm{var}} \left(
\sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} \alpha_R(j) \times T_R(j)
\right)$">|; 

$key = q/f(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img53.svg"
 ALT="$f(j)$">|; 

$key = q/f(j)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img54.svg"
 ALT="$f(j) = 0 $">|; 

$key = q/f(j)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img55.svg"
 ALT="$f(j) = 1 $">|; 

$key = q/f_{{ensuremath{mathrm{off}}{,S_{{ensuremath{mathrm{in}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.50ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img113.svg"
 ALT="$f_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{in}}}}$">|; 

$key = q/f_{{ensuremath{mathrm{off}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.50ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img112.svg"
 ALT="$f_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/f_{{ensuremath{mathrm{off}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img114.svg"
 ALT="$f_{\ensuremath{\mathrm{off}}}$">|; 

$key = q/f_{{ensuremath{mathrm{rest}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img122.svg"
 ALT="$f_{\ensuremath{\mathrm{rest}}}$">|; 

$key = q/f_{{ensuremath{mathrm{res}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.50ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img111.svg"
 ALT="$f_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/f_{{ensuremath{mathrm{res}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img8.svg"
 ALT="$f_{\ensuremath{\mathrm{res}}}$">|; 

$key = q/fne0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img100.svg"
 ALT="$f \ne 0$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.76ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img44.svg"
 ALT="$i$">|; 

$key = q/i_{{ensuremath{mathrm{chan}}{}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.11ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img117.svg"
 ALT="$i_{\ensuremath{\mathrm{chan}}} = 0$">|; 

$key = q/j_{{ensuremath{mathrm{max}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.21ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img39.svg"
 ALT="$j_{\ensuremath{\mathrm{max}}}$">|; 

$key = q/j_{{ensuremath{mathrm{min}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.21ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img38.svg"
 ALT="$j_{\ensuremath{\mathrm{min}}}$">|; 

$key = q/k_{{ensuremath{mathrm{max}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.19ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img41.svg"
 ALT="$k_{\ensuremath{\mathrm{max}}}$">|; 

$key = q/k_{{ensuremath{mathrm{min}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.19ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img40.svg"
 ALT="$k_{\ensuremath{\mathrm{min}}}$">|; 

$key = q/mu_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.68ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\mu_R$">|; 

$key = q/obs;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img102.svg"
 ALT="$obs$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img109.svg"
 ALT="$r$">|; 

$key = q/r_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img15.svg"
 ALT="$r_R$">|; 

$key = q/r_T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img16.svg"
 ALT="$r_T$">|; 

$key = q/reso(resampled)slashreso(input);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img5.svg"
 ALT="$reso(resampled)/reso(input)$">|; 

$key = q/sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\sigma$">|; 

$key = q/sigma_R(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img90.svg"
 ALT="$\sigma_R(j)$">|; 

$key = q/sigma_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img48.svg"
 ALT="$\sigma_R$">|; 

$key = q/sigma_{R'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img80.svg"
 ALT="$\sigma_{R'}$">|; 

$key = q/sigma_{R'}=sigma_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img83.svg"
 ALT="$\sigma_{R'} = \sigma_R$">|; 

$key = q/sigma_{R'}=sigma_Rslashsqrt{1.6};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.91ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img86.svg"
 ALT="$\sigma_{R'} = \sigma_R / \sqrt{1.6}$">|; 

$key = q/sigma_{R'}=sigma_Rslashsqrt{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.91ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img89.svg"
 ALT="$\sigma_{R'} = \sigma_R / \sqrt{2}$">|; 

$key = q/sqrt{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.64ex; vertical-align: -0.42ex; " SRC="|."$dir".q|img92.svg"
 ALT="$\sqrt{2}$">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.66ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img7.svg"
 ALT="$t$">|; 

$key = q/t_{S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img105.svg"
 ALT="$t_{S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/textstyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.08ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\textstyle =$">|; 

$key = q/ttimesf_{{ensuremath{mathrm{res}}{}slashT_{{ensuremath{mathrm{sys}}{}^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.00ex; vertical-align: -1.01ex; " SRC="|."$dir".q|img6.svg"
 ALT="$t \times f_{\ensuremath{\mathrm{res}}} / T_{\ensuremath{\mathrm{sys}}}^2$">|; 

$key = q/ttimes|r|slashT_{{ensuremath{mathrm{sys}}{}^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.00ex; vertical-align: -1.01ex; " SRC="|."$dir".q|img108.svg"
 ALT="$t \times \vert r\vert / T_{\ensuremath{\mathrm{sys}}}^2$">|; 

$key = q/v_{{ensuremath{mathrm{off}}{,S_{{ensuremath{mathrm{in}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img124.svg"
 ALT="$v_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{in}}}}$">|; 

$key = q/v_{{ensuremath{mathrm{off}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img123.svg"
 ALT="$v_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/v_{{ensuremath{mathrm{off}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img125.svg"
 ALT="$v_{\ensuremath{\mathrm{off}}}$">|; 

$key = q/v_{{ensuremath{mathrm{res}}{,S_{{ensuremath{mathrm{out}}{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img119.svg"
 ALT="$v_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$">|; 

$key = q/w(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img34.svg"
 ALT="$w(i)$">|; 

$key = q/w_R(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img50.svg"
 ALT="$w_R(i)$">|; 

$key = q/w_R(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img95.svg"
 ALT="$w_R(j)$">|; 

$key = q/w_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img98.svg"
 ALT="$w_S$">|; 

$key = q/w_{R'}(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img63.svg"
 ALT="$w_{R'}(i)$">|; 

$key = q/w_{R'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img79.svg"
 ALT="$w_{R'}$">|; 

$key = q/w_{R'}=1.6timesw_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img85.svg"
 ALT="$w_{R'} = 1.6 \times w_R$">|; 

$key = q/w_{R'}=2timesw_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img88.svg"
 ALT="$w_{R'} = 2 \times w_R$">|; 

$key = q/w_{R'}=w_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img82.svg"
 ALT="$w_{R'} = w_R$">|; 

$key = q/w_{R'}slashw_{R};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img91.svg"
 ALT="$w_{R'}/w_{R}$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img30.svg"
 ALT="$x$">|; 

$key = q/x_{{ensuremath{mathrm{min}}{,S};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.89ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img29.svg"
 ALT="$x_{\ensuremath{\mathrm{min}},S}$">|; 

$key = q/x_{{ensuremath{mathrm{val}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.58ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img78.svg"
 ALT="$x_{\ensuremath{\mathrm{val}}}$">|; 

$key = q/x_{{ensuremath{mathrm{val}}{}=f_{{ensuremath{mathrm{res}}{}times(0-r_{{ensuremath{mathrm{chan}}{})+f_{{ensuremath{mathrm{off}}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.55ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img118.svg"
 ALT="$x_{\ensuremath{\mathrm{val}}} = f_{\ensuremath{\mathrm{res}}} \times
(0 -r_{\ensuremath{\mathrm{chan}}}) + f_{\ensuremath{\mathrm{off}}}$">|; 

$key = q/x_{{ensuremath{mathrm{val}}{}rightarrowx_{{ensuremath{mathrm{val}}{}+0.00;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img81.svg"
 ALT="$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.00$">|; 

$key = q/x_{{ensuremath{mathrm{val}}{}rightarrowx_{{ensuremath{mathrm{val}}{}+0.25;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img84.svg"
 ALT="$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.25$">|; 

$key = q/x_{{ensuremath{mathrm{val}}{}rightarrowx_{{ensuremath{mathrm{val}}{}+0.50;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img87.svg"
 ALT="$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.50$">|; 

$key = q/{R'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.97ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img74.svg"
 ALT="${R'}$">|; 

1;

