 of modems for transmitting data over analogue telephone cir- cuits. This response has its maximum at t=0 (where h(0) = 1) and is An important example of the use of a digital carrier for transmit- zero for t given by Equation 19.6 where T is as in Equation 19.7. ting an analogue baseband signal is the use of pulse code modulation (PCM) for sending voice signals over digital circuits. This enables t==nT (19.6) telephony to obtain the advantages of digital transmission, namely effective immunity to distortion, interference, crosstalk and noise T=12W (19.7) and a constant transmission performance regardless of the length of a telephone connection and its routeing. If pulses are transmitted at rate B = 2W and each is detected by sampling at the time when it has its maximum output voltage, the 19.2 Digital transmission outputs due to all preceding and following pulses are zero at that time, i.e. there is no intersymbol interference (ISI). Thus, it is possible to transmit pulses at rate B bauds through a channel of In a digital transmission system, a modulator lies between the bandwidth W = 1/2B without any ISI. baseband input channel and the transmission path and a demodula- In practice, it is not possible to obtain a channel with an ideal low tor lies between that and the baseband output channel. The baseband pass characteristic. (Equation 19.5 shows that, if it were possible, an input signal and the modulator determine the form of the transmitted output voltage would appear before the input pulse is applied!) signal and the demodulator is required to reconstruct the baseband However, Nyquist showed that zero ISI can also be obtained if the signal with adequate fidelity. The overall channel between the gain of the channel changes from unity to zero over a band of modulator input and demodulator output must have the required frequencies with a gain frequency response that is skew symmetri- properties and these will now be considered. cal about f = 1/2B. It is also impossible to generate a perfect impulse (since it has