A sequence of digital symbols becomes a continuous-time baseband waveform by assigning a pulse to each symbol interval.

A common model is

$$x(t)=\sum_k a_k p(t-kT_s),$$

where $a_k$ are symbol values, $T_s$ is the symbol interval and $p(t)$ is the pulse shape.

If the pulse extends beyond one symbol interval, neighboring pulses overlap. Overlap is not automatically harmful: what matters is whether contributions from other symbols remain at the receiver's decision instant.

Unwanted contribution from neighboring symbols is intersymbol interference, or ISI.

Pulse shape affects both time-domain interference and occupied spectrum. Abrupt narrow pulses can require large bandwidth, while smoother band-limited pulses spread farther in time.

Pulse shaping is therefore a controlled time-frequency trade-off. The transmitter and receiver choose waveforms so symbols can be distinguished at the desired rate within the available channel bandwidth.