What happens when is fed into the LSI system?

Lets look at the convolution of the impulse response h(t) of the Ideal low-pass filter with

where we have seen .

When is passed through a Low pass filter, the output which is the reconstructed signal is nothing but the sum of copies of the impulse response h(t) shifted by integral multiples of and multiplied by the value of x(t) at the corresponding integral multiple of . Also observe that the h(t) is zero at all sample points (which are integral multiples of ) except at zero. Thus, the reconstruction of x(t) can be visualized as a sum of the following signals :