Symbol for Fourier pair as per Brigham, "The Fast Fourier Transform"

You could build something from a picture environment.

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{pict2e}
\makeatletter
\newlength{\fsize}
\setlength{\fsize}{\f@size pt}
\newcommand*{\Fp@ir}[2][.4]{%
    \setlength{\unitlength}{#2\fsize}%
    \begin{picture}(1.5,1)(0,.12)
        \roundcap\linethickness{#1 pt}
        \put( 0,.5){\line(1, 1.5){.25}}
        \put( 0,.5){\line(1,-1.5){.25}}
        \put(.1,.5){\line(1, 1.5){.2}}
        \put(.1,.5){\line(1,-1.5){.2}}
        \put(.25,.88){\line(1,0){1}}
        \put(.25,.12){\line(1,0){1}}
        \put(.3,.2){\line(1,0){.9}}
        \put(.3,.8){\line(1,0){.9}}
        \put(1.5,.5){\line(-1, 1.5){.25}}
        \put(1.5,.5){\line(-1,-1.5){.25}}
        \put(1.4,.5){\line(-1, 1.5){.2}}
        \put(1.4,.5){\line(-1,-1.5){.2}}
    \end{picture}%
}
\newcommand*{\Fpair}{\mathchoice%
    {\mathrel{\Fp@ir{1}}}%
    {\mathrel{\Fp@ir{1}}}%
    {\mathrel{\Fp@ir[.3]{.7}}}%
    {\mathrel{\Fp@ir[.25]{.5}}}%
}
\makeatother
\begin{document}
\( \displaystyle a \Fpair b \)
\( \textstyle a \Fpair b \)
\( \scriptstyle a \Fpair b \)
\( \scriptscriptstyle a \Fpair b \)
\end{document}

The closest thing to that in Unicode is ⏣, the symbol for a benzene ring, which is \benzener in unicode-math, stix or stix2. You could define it as \mathbin{\benzener} or even stretch it out horizontally with a \scalebox.

Or you could draw it in TikZ.

From the suggestion of very good user @Davislor, I have created a symbol named \benz not very similar to your picture.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\usepackage{scalerel}
\newcommand{\benz}{\mathbin{\hstretch{3}{\scalebox{.4}{\begin{tikzpicture}
% create the node
\node[draw=black,minimum size=.7cm,regular polygon,regular polygon sides=6] (a) {};
\node[draw=black,minimum size=.55cm,regular polygon,regular polygon sides=6] (a) {};
\end{tikzpicture}}}}}
\begin{document}

$a\benz b$
\end{document}