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}
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}
\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.