A request for an example of a band limited signal.

Question

Recall that a signal $x(t)$ is band-limited signal if its Fourier transform $$ X_{\Phi}(\Omega)=\int_{-\infty}^{\infty}x(t)e^{-j\Omega t}dt $$ vanishes outside an interval, say $[-\Omega_0,\Omega_0]$. The problem is that I can not find any examples for such signals ! Even "simple" example such as $$ x(t)= \begin{cases} 1 & t\in[0,T]\\ 0 & otherwise \end{cases} $$ is not band-limited signal. I would appreciate it if someone could write me examples of such signals