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Concept
Pulse shaping
Summary
In electronics and telecommunications, pulse shaping is the process of changing a transmitted pulses' waveform to optimize the signal for its intended purpose or the communication channel. This is often done by limiting the bandwidth of the transmission and filtering the pulses to control intersymbol interference. Pulse shaping is particularly important in RF communication for fitting the signal within a certain frequency band and is typically applied after line coding and modulation.
Transmitting a signal at high modulation rate through a band-limited channel can create intersymbol interference. The reason for this are Fourier correspondences (see Fourier transform). A bandlimited signal corresponds to an infinite time signal, that causes neighbouring pulses to overlap. As the modulation rate increases, the signal's bandwidth increases. As soon as the spectrum of the signal is a sharp rectangular, this leads to a sinc shape in the time domain. This happens if the bandwidth of the signal is larger than the channel bandwidth, leading to a distortion. This distortion usually manifests itself as intersymbol interference (ISI). Theoretically for sinc shaped pulses, there is no ISI, if neighbouring pulses are perfectly aligned, i.e. in the zero crossings of each other. But this requires a very good synchronization and precise/stable sampling without jitters. As a practical tool to determine ISI, one uses the Eye pattern, that visualizes typical effects of the channel and the synchronization/frequency stability.
The signal's spectrum is determined by the modulation scheme and data rate used by the transmitter, but can be modified with a pulse shaping filter. This pulse shaping will make the spectrum smooth, leading to a time limited signal again. Usually the transmitted symbols are represented as a time sequence of dirac delta pulses multiplied with the symbol. This is the formal transition from the digital to the analog domain. At this point, the bandwidth of the signal is unlimited.
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