2.3.3 Bandwidth Of Baseband Digital Signals
In baseband transmission, the digital waveform is transmitted directly over the communications channel without first being translated to a higher-frequency carrier. The occupied bandwidth is therefore determined primarily by two factors: the symbol rate and the shape of the transmitted pulses. Faster symbol rates require the pulses to become shorter in time, and shorter pulses contain a broader range of frequency components. Consequently, increasing the data rate inevitably increases the bandwidth required to transmit the signal faithfully.
This relationship between signaling speed and bandwidth is one of the fundamental constraints in communications engineering. Every practical communication channel has a finite bandwidth, determined by the physical characteristics of the transmission medium and the equipment connected to it. If the transmitted signal occupies more bandwidth than the channel can support, the higher-frequency components are attenuated. As discussed in the previous section, this causes the transmitted pulses to spread in time and overlap adjacent symbols, producing inter-symbol interference (ISI) and increasing the probability of detection errors.
For an ideal noiseless channel of bandwidth (B), the Nyquist criterion states that symbols can be transmitted without inter-symbol interference at a maximum symbol rate of:
where Rs is the symbol rate (baud) and B is the channel bandwidth in hertz.
This result establishes a fundamental relationship between bandwidth and signaling speed: doubling the symbol rate requires approximately twice the channel bandwidth. Equivalently, for a given channel bandwidth there is a maximum symbol rate beyond which reliable transmission is no longer possible unless more sophisticated signaling techniques are employed.
It is important to recognize that the Nyquist criterion represents an ideal theoretical limit. It assumes a perfectly noiseless channel together with ideal pulse shaping and perfectly synchronized transmission and reception. Real communication systems cannot satisfy these assumptions exactly. Practical filters have finite roll-off characteristics, synchronization is never perfect, and communication channels inevitably introduce attenuation, distortion, and noise. Consequently, practical systems generally require additional bandwidth beyond the Nyquist minimum to achieve reliable operation.
Fortunately, engineers have developed pulse-shaping techniques that allow practical systems to approach this theoretical limit quite closely. Raised-cosine and root-raised-cosine filtering, introduced in the previous section, are widely used because they minimize inter-symbol interference while requiring only a modest increase in bandwidth. These techniques are employed in many modern communication systems, including digital radio, satellite communications, optical fiber links, and cellular networks.
The Nyquist criterion therefore provides an important benchmark for communication system design. It establishes the minimum bandwidth required to support a given symbol rate under ideal conditions and serves as a reference against which practical systems can be compared. In the next section we consider a second fundamental limitation: even if sufficient bandwidth is available, the presence of noise places an additional limit on the amount of information that can be transmitted reliably. This limit is described by the Shannon–Hartley theorem.
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