Time-discrete samples and continuous time

Summary

A bandlimited pulse is infinitely long on a continuous-time axis.
Sampled at the correct rate and phase, only a single sample remains. All others fall onto zero crossings.
When sampling rate or phase are changed, the full length becomes visible.
This is a consequence of the Nyquist pulse-shaping criterion.

Figure 1 shows a bandlimited pulse on a continuous time axis.

Figure 1: Bandlimited continuous-time pulse

It is converted to time-discrete samples in Figure 2.

Figure 2: Samples taken from Figure 1

Only a single sample is non-zero, all others fall onto zero crossings (figure 3).

Figure 3: Samples fall on zero crossings

This is a consequence of Nyquist's pulse shaping criterion.
Both sample rate and phase meet the criterion.

Increasing the sampling rate or changing the phase will violate the pulse shaping criterion, and an infinite number of samples becomes visible.
In general, no information is lost, because the operation can be reversed.

© Markus Nentwig 2007-2008
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