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

I'm looking for a specific symbol used to denote a Fourier transform pair in the book:

Brigham, E. O. (1974). "The Fast Fourier Transform", Prentice-Hall. Englewood Cliffs, NJ, 19742.

It looks like this:

I searched extensively on the Comprehensive LaTeX Symbol List by Scott Pakin, but to no avail. I'm not even sure that this symbol exist, but, by chance, does anybody recognise it?

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}

• Wonderful....very very nice. Dec 28, 2020 at 20:39
• Wow, yes, this is definitely an all-in-one solution. Thank you @Vincent! Dec 28, 2020 at 22:03

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}


• Very lazy user Davislor approves! Dec 28, 2020 at 13:03
• @Davislor ahahahahah.LOL...But it is not very good my code...but I think that putting the original symbol near a and b it is very ugly. Otherwise the user can you put the image scaling using \includegraphics. Dec 28, 2020 at 13:05
• This is very ingenious, to say the least. I tried to tweak the proportions, but i still couldn't get it just the same as the one from the book. Still, I'm definitely saving this, I learned something from it! Dec 28, 2020 at 22:02
• @IsaiaIsmaele Thank you very much for your nice words. All the best. Dec 28, 2020 at 22:21