How to set the space between rows in a table

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\subsubsection*{Fourier Transform properties}
{\def\arraystretch{2}\tabcolsep=10pt
\begin{tabular}{@{}l | l | l | l @{}}
    Property & Time domain & Frequency domain & Condition \\
    \hline
    Time-shift & $f(t - \tau)$ & $\hat{f}(\omega)e^{-i \omega \tau}$ \\
    Frequency-shift & $f(t) e^{i \omega_0 t}$ & $\hat{f}(\omega - \omega_0)$ \\
\rule{0pt}{5ex}%  EXTRA vertical height  
    Modulation Thm. & $f(t)\cos(\omega_0 t)$ & $\dfrac{ \hat{f}(\omega-\omega_0)+\hat{f}(\omega+\omega_0) }{2}$ \\
    Differentiation (time) & $f^{(n)}(t)$ & $(i\omega)^n \hat{f}(\omega)$ & $\displaystyle\lim_{\mathclap{t \to \pm \infty}} f(t) = 0$
\end{tabular}%
}
\end{document}

enter image description here

another possibility is to use package tabls. But this may cause problems when using other tabular packages. Try it and maybe the possible optional arguments are of interest, as minimal distance between tabulkar lines.

\documentclass{article}

\usepackage{mathtools}
\usepackage{tabls}

\begin{document}

\subsubsection*{Fourier Transform properties}
{\tablinesep=2ex\tabcolsep=10pt
\begin{tabular}{@{}l | l | l | l @{}}
    Property & Time domain & Frequency domain & Condition \\
    \hline
    Time-shift & $f(t - \tau)$ & $\hat{f}(\omega)e^{-i \omega \tau}$ \\
    Frequency-shift & $f(t) e^{i \omega_0 t}$ & $\hat{f}(\omega - \omega_0)$ \\   
    Modulation Thm. & $f(t)\cos(\omega_0 t)$ & $\dfrac{ \hat{f}(\omega-\omega_0)+\hat{f}(\omega+\omega_0) }{2}$ \\
    Differentiation (time) & $f^{(n)}(t)$ & $(i\omega)^n \hat{f}(\omega)$ & $\displaystyle\lim_{\mathclap{t \to \pm \infty}} f(t) = 0$
\end{tabular}%
}
\end{document}

enter image description here


\extrarowheight does add the same amount of space to each row, but the fraction \frac{\hat{f}(\omega-\omega_0)+\hat{f}(\omega+\omega_0)}{2} makes for a rather unappealing table. For better appearance, you might prefer something like that:

\documentclass{article}

\usepackage{amsmath}
\usepackage{tabularx}
\usepackage{array}
\usepackage[top=0.5cm, bottom=0.5cm, left=0.5cm, right=0.5cm, columnsep=0.75cm]{geometry}

\begin{document}

\subsubsection*{Fourier Transform properties}
{
\setlength{\extrarowheight}{.5em}
\begin{tabular}{l@\quad|@\quad l@\quad|@\quad l@\quad|@\quad l}
    Property & Time domain & Frequency domain & Condition \\
    \hline
    Time-shift & $f(t - \tau)$ & $\hat{f}(\omega)e^{-i \omega \tau}$ \\
    Frequency-shift & $f(t) e^{i \omega_0 t}$ & $\hat{f}(\omega - \omega_0)$ \\
    Modulation Thm. & $f(t)\cos(\omega_0 t)$ &
        $\left[\hat{f}(\omega-\omega_0)+\hat{f}(\omega+\omega_0)\right]/\,2$ \\
    Differentiation (time) & $f^{(n)}(t)$ &
        $(i\omega)^n \hat{f}(\omega)$ & $\lim_{t \to \pm \infty} f(t) = 0$
\end{tabular}

\end{document}

EDIT: thanks to those users who posted constructive suggestions below. enter image description here

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Spacing

Tables