Underbrace under sqrt content

Question

I am trying to use underbrace to clarify the arguments to a sqrt. However this causes the square root sign to reach all the way down to the bottom of the text under the brace(s), which is not what I want.

MWE:

\documentclass{article}
\usepackage{mathtools}

\begin{document}

$\sqrt{\underbrace{\frac{1}{\tau}\underbrace{\int_{\text{-}\infty}^{t}\underbrace{p_{X}^{\,2}\left(\xi\right)\cdot e^{\frac{\text{-}\left(t\text{-}\xi\right)}{\tau}}}_{\substack{\text{Expontial}\\\text{time-weighting}\\\text{of $p_{X}^{\,2}\left(\xi\right)$}}} \,\mathrm{d}\xi}_{\text{Exponential integration}}}_{\substack{\text{Exponential averaging}\\\text{= “Quasi mean-square”}}}}$

\end{document}

This results in something like this:

Does anyone know how I can force sqrt to reach only as low as its actual (mathematically speaking) argument?

Answer 1

I would recommend Mico's way; if you really want the surd, then here is a solution that takes all the vertical space it needs (not like in wh1t3's answer):

\documentclass{article}
\usepackage{mathtools}

\def\sqrtexplained#1{%
  \begingroup
    \sbox0{$#1$}
    \def\underbrace##1_##2{##1}
    \sbox2{$#1$}
    \dimen0=\wd0 \advance\dimen0-\wd2
    \mathrlap{\sqrt{\phantom{\displaystyle#1}\kern\dimen0 }}
    \hphantom{\sqrt{\vphantom{\displaystyle#1}}}
  \endgroup
  #1}


\begin{document}

\[
\sqrtexplained{%
\underbrace{\frac{1}{\tau}
  \underbrace{\int_{-\infty}^{t}
    \underbrace{p_{X}^{2}(\xi)\cdot e^{\frac{-(t-\xi)}{\tau}}}
    _{\substack{\text{Exponential}\\
                \text{time-weighting}\\
                \text{of $p_{X}^{2}(\xi)$}}
     }
   \,\mathrm{d}\xi}
   _{\text{Exponential integration}}}
_{\substack{\text{Exponential averaging}\\
            =\text{Quasi mean-square}}
 }
}
\]

\end{document}

I've also corrected the input errors you are making: \text{-} for a minus sign is wrong; \left and \right should be used only when they are really needed.

Answer 2

I would suggest that you not use the \sqrt{...} symbolism at all because it adds yet another horizontal bar to an expression that's already very busy-looking. Instead, I suggest you write something like:

\documentclass{article}
\usepackage{concrete,eulervm,mathtools}
\begin{document}
$ \biggl(\,
   \underbrace{\frac{1}{\tau} 
   \underbrace{\int\limits_{-\infty}^{t}
   \underbrace{p_{X}^{\,2} (\xi) \cdot e^{-(t-\xi)/\tau}}
      _{\substack{\text{Exponential time-}\\
                  \text{weighting of $p_{X}^{\,2}(\xi)$}}} 
   \,d\xi}
      _{\text{Exponential integration}}}
      _{\substack{\text{Exponential averaging}\\
                  \text{$=$ ``Quasi mean-square''}}}
  \,\biggr)^{1/2} $
\end{document}

Answer 3

You can use \smash and a \vphantom to make it work.

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\[\sqrt{\vphantom{\int_{\text{-}\infty}^{t}x}\smash{
  \underbrace{
    \frac{1}{\tau}
    \underbrace{
      \int_{\text{-}\infty}^{t}
      \underbrace{
        p_{X}^{\,2}\left(\xi\right)\cdot e^{\frac{\text{-}\left(t\text{-}\xi\right)}{\tau}}
        }_{\substack{\text{Expontial}\\\text{time-weighting}\\\text{of $p_{X}^{\,2}\left(\xi\right)$}}} \,\mathrm{d}\xi
      }_{\text{Exponential integration}}
    }_{\substack{\text{Exponential averaging}\\\text{= “Quasi mean-square”}}}
  }}\]

\end{document}

The output looks like this:

I should note that this does not appear to work in inline math-mode. The size of the vphantom does not correctly reflect the integral sign then. Perhaps someone else can explain why this is the case, since I don't know.

Edit after @egreg's comment, an additional vphantom should be added, to ensure the displaymath gets the height of the braces as well. The modified code would look like this:

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\[\sqrt{\vphantom{\int_{\text{-}\infty}^{t}x}\smash{
  \underbrace{
    \frac{1}{\tau}
    \underbrace{
      \int_{\text{-}\infty}^{t}
      \underbrace{
        p_{X}^{\,2}\left(\xi\right)\cdot e^{\frac{\text{-}\left(t\text{-}\xi\right)}{\tau}}
        }_{\substack{\text{Expontial}\\\text{time-weighting}\\\text{of $p_{X}^{\,2}\left(\xi\right)$}}} \,\mathrm{d}\xi
      }_{\text{Exponential integration}}
    }_{\substack{\text{Exponential averaging}\\\text{= “Quasi mean-square”}}}
  }}
  \vphantom{\underbrace{
    \frac{1}{\tau}
    \underbrace{
      \int_{\text{-}\infty}^{t}
      \underbrace{
        p_{X}^{\,2}\left(\xi\right)\cdot e^{\frac{\text{-}\left(t\text{-}\xi\right)}{\tau}}
        }_{\substack{\text{Expontial}\\\text{time-weighting}\\\text{of $p_{X}^{\,2}\left(\xi\right)$}}} \,\mathrm{d}\xi
      }_{\text{Exponential integration}}
    }_{\substack{\text{Exponential averaging}\\\text{= “Quasi mean-square”}}}
  }
  \]

  A long sentence after it to see if there are problems with overruning.

\end{document}

And its output like this:

Answer 4

Seems to be missing a tikz solution:

or with smaller text under the brace:

Code:

\documentclass{article}
\usepackage{mathtools}
\usepackage{xparse}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathreplacing}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}

% Tweak these as necessary
\newcommand*{\BraceAmplitude}{0.4em}%
\newcommand*{\VerticalOffset}{0.8ex}%  
\newcommand*{\HorizontalOffset}{0.0em}% 


\NewDocumentCommand{\InsertUnderBrace}{%
    O{} % #1 = draw options
    O{yshift=0.0cm} % #2 = optional brace shift options
    m   % #3 = left tikzmark
    m   % #4 = right tikzmark
    m   % #5 = text to place under brace
}{%
    \begin{tikzpicture}[overlay,remember picture]
    \draw [densely dotted, draw=blue, text=black, #1] 
        ($(#4)+(\HorizontalOffset,-\VerticalOffset)$) --
        ([#2]$(#4)+(\HorizontalOffset,-\VerticalOffset)$);
    \draw [decoration={brace, amplitude=\BraceAmplitude}, decorate, thick, draw=blue, text=black, #1]
        ([#2]$(#4)+( \HorizontalOffset,-\VerticalOffset)$) -- 
        ([#2]$(#3)+(-\HorizontalOffset,-\VerticalOffset)$)
        node [below=\VerticalOffset, midway, align=center] {#5};
    \draw [densely dotted, draw=blue, text=black, #1] 
        ([#2]$(#3)+(-\HorizontalOffset,-\VerticalOffset)$) --
        ($(#3)+(\HorizontalOffset,-\VerticalOffset)$);
    \end{tikzpicture}%
}%

\newcommand*{\MyEquation}{%
    \tikzmark{StartBraceC}
    \sqrt{%
        \frac{1}{\tau} 
        \tikzmark{StartBraceB}
        \int_{\text{-}\infty}^{t} 
            \tikzmark{StartBraceA}
                p_{X}^{2}
                \left(\xi\right)
                \cdot e^{\frac{\text{-}\left(t\text{-}\xi\right)}{\tau}} 
            \tikzmark{EndBraceA}
            \mathrm{d}\xi
        \tikzmark{EndBraceB}
    }
    \hspace*{0.5em}\tikzmark{EndBraceC}
}
\begin{document}
\[ \MyEquation \]
%
\InsertUnderBrace[draw=red,text=red]{StartBraceA}{EndBraceA}
    {Exponential \\ time-weighting \\ of $p_{X}^{\,2}\left(\xi\right)$}
%
\InsertUnderBrace[draw=olive,text=olive][yshift=-1.5cm]{StartBraceB}{EndBraceB}
    {Exponential \\ integration}
%
\InsertUnderBrace[draw=blue,text=blue][yshift=-2.5cm]{StartBraceC}{EndBraceC}
    {Exponential averaging \\= ``Quasi mean-square"}
%
\vspace*{3.0cm}\par
\bigskip\noindent
or with smaller text
\[ \MyEquation \]
%
\InsertUnderBrace[draw=red,text=red, font=\tiny]{StartBraceA}{EndBraceA}
    {Exponential time-\\weighting of $p_{X}^{\,2}\left(\xi\right)$}
%
\InsertUnderBrace[draw=olive,text=olive, font=\tiny][yshift=-0.8cm]{StartBraceB}{EndBraceB}
    {Exponential integration}
%
\InsertUnderBrace[draw=blue,text=blue, font=\tiny][yshift=-1.4cm]{StartBraceC}{EndBraceC}
    {Exponential averaging = ``Quasi mean-square"}
\end{document}

Answer 5

If you would like to have nice looking braces then you can use the following brute force method.

\documentclass{article}
\usepackage{mathtools}
\usepackage{pstricks}
\usepackage{pstricks-add}

\begin{document}

\begin{pspicture*}(-5,-5)(5,5)
\(\sqrt{\frac{1}{\tau}\int_{-\infty}^{t} p_{X}^{2}(\xi)\cdot e^{t-\xi}d\xi}\)
\psbrace[rot=90, braceWidthInner=5pt, braceWidthOuter=5pt, nodesepB=8pt, nodesepA=-15pt]   (-2.5,-.2)(-.5,-.2){some text}
\end{pspicture*}

\end{document}