The impulse response of the ideal low pass filter extends to. If the impulse response is denoted by h(t), the output signal y(t) corresponding to input signal x(t) is given by :

The value of y at any t depends on values of x all the way to if h(t) extends to . Thus realization in real time is not possible for an Ideal low-pass filter. In other words, unless one knows the entire , reconstruction cannot be done.

Note if h(t) had been finitely non-causal (say zero for all t less than some - ), then real time realization would have been possible subject to a time-delay (of ).

It can be shown that diverges.

This implies that bounded input does not imply bounded output. Thus if we build an oscillator with Ideal Low pass Filter a bounded input may result in an unstable output.

That means, it is not exactly realizable with simple well known elements .

We will get back to how these problems are tackled a little later. In the next lecture, we move on to the problem of impulses not being physically realizable.