Inverse DTFT low pass filter
Since the impulse response of an ideal low pass filter extends to plus and minus infinity, the corresponding filter is not causal, i.e., in order to implement it (exactly) you would need to know the complete input signal (including its future) to compute the current output value. Furthermore, the sinc function only decays as $1/n$, which makes the filter unstable. In sum, the ideal low pass filter is non-causal and unstable, and for that reason it can't be implemented. Of course, we can approximately implement it by making it causal and stable in such a way that its desirable characteristics are not changed too much for the given application. That's the topic of the field filter design. An little overview for the discrete-time case can be found here.