A pulse can overlap neighboring symbol intervals yet produce no intersymbol interference at the sampling instants.

For effective received pulse $g(t)$ and symbol interval $T_s$, the zero-ISI condition is

$$g(nT_s)=0\qquad\text{for every nonzero integer }n,$$

with

$$g(0)\ne 0.$$

At the decision time for symbol $a_k$, every shifted pulse from another symbol then contributes zero, so the sampled value depends only on $a_k$.

A rectangular frequency response leads to a sinc-shaped time-domain pulse, which satisfies this sampling condition but decays slowly. Practical systems often use raised-cosine families that trade excess bandwidth for faster time-domain decay.

The roll-off factor controls that trade-off: more excess bandwidth gives a pulse that is less extended in time and therefore more tolerant of implementation imperfections.

This Nyquist criterion concerns symbol pulses and ISI. It is distinct from the Nyquist-Shannon sampling theorem for reconstructing a continuous-time signal from samples.