Pulseshaping

Pulseshaping is the design of the temporal envelope of transmitted pulses to control the spectral occupancy of a signal and to minimize intersymbol interference (ISI) in communication systems. In digital communications, information is carried by a sequence of symbols that are mapped to waveforms; the chosen pulse shape determines the signal bandwidth and how strongly adjacent symbols interfere with each other. The aim is to approach the Nyquist criterion for zero ISI, so that the combined response of the transmitter, channel, and receiver yields clean symbol sampling at the receiver.

Theoretical basis centers on ensuring that pulses spaced by the symbol interval T do not cause interference at the sampling instants. In practice, this is achieved by shaping each symbol with a pulse p(t) whose Fourier spectrum confines energy within a desired bandwidth while satisfying sampling properties that cancel ISI at symbol times when combined with a suitable receiver filter.

Common pulse shapes include raised cosine (RC) and root raised cosine (RRC). The RC shape has a controllable roll-off factor that sets excess bandwidth beyond the minimum Nyquist bandwidth. The RRC shape is used in pairs ( transmitter and receiver) so that their cascade yields a raised cosine response, providing practical zero-ISI behavior with finite-length filters. Gaussian pulse shaping is used in some modulation schemes (notably in GMSK) for its good spectral efficiency, though it does not achieve ideal zero-ISI by itself. Sinc pulses are the theoretical ideal but have infinite duration and are impractical.

Implementation typically uses finite impulse response (FIR) or equivalent filters in digital transceivers, with design choices reflecting trade-offs between bandwidth efficiency, out-of-band emissions, and resilience to channel distortion. Pulseshaping is fundamental in many domains, including wireless, wired digital communications, and optical systems.