The Engineer's Guide to Standards Conversion - Snell

A single pixel has meaning over the two dimensions of a frame and along the
time axis. If this were not true, it would be impossible to build an interpolator. If
the cut-off frequency of the filter is one-half of the sampling rate, the impulse
response passes through zero at the sites of all other samples.
Sample
Analogue output
Sinx/ x
impulses
due to sample
etc.
etc.
Fig 3.1.2
In a reconstruction filter, the impulse response is such that it passes
through zero at the sites of adjacent samples. Thus the output
waveform joins up the tops of the samples as required.
It can be seen from Fig 3.1.2 that at the output of such a filter, the voltage at the
centre of a sample is due to that sample alone, since the value of all other samples is
zero at that instant. In other words the continuous time output waveform must join
up the tops of the input samples. In between the sample instants, the output of the
filter is the sum of the contributions from many impulses, and the waveform
smoothly joins the tops of the samples. If the waveform domain is being considered,
the anti-image filter of the frequency domain can equally well be called the
reconstruction filter. It is a consequence of the band-limiting of the original antialiasing
filter that the filtered analogue waveform could only travel between the
sample points in one way.
30