Changing the Bandwidth of a signal of fixed Sampling frequency
given sample rate $f_\text{s}$, this

$$ x(t) = \sum\limits_{n=-N}^{+N} x[n] \operatorname{sinc}\left(2 B \left(t-\tfrac{n}{f_\text{s}}\right)\right) $$

is bandlimited to $\pm B$, no matter what the numbers $x[n]$ are.  $N\ge0$ can be as little or as large as you want.

it might have bandwidth of $B$ if the values of $x[n]$ are sufficiently white or with high-enough content at high frequencies.  but the one-sided bandwidth will not exceed $B$.

forgot to be explicit.  the sinc function is:

$$ \operatorname{sinc}(u) \triangleq \begin{cases}
\frac{\sin(\pi u)}{\pi u} \qquad &amp; u \ne 0 \\
\\ 
1 &amp; u = 0 \\
\end{cases} $$